% BibTeX database kpath.bib
% exported by BibGene 1.2.2, Mon, Mar 19, 2001.
% Bibliography on k shortest paths and other "k best solutions" problems
% David Eppstein, Univ. of Calif., Irvine, Dept. Information & Computer Sci.,
% http://www.ics.uci.edu/~eppstein/
@phdthesis{Abd-PhD-88,
title = {{A Dual-Based Approach to a Multiobjective Location Problem}},
author = {Bahgat Abdel-Hameed Abdel-Lateef},
school = {Univ. of Liverpool, Dept. of Mathematics},
year = {1988},
abstract = {The work presented in this thesis is concerned with the use
of dual-based approaches for solving Multi-objective Location Problems
which may be used to represent many real life location Problems. In particular,
attention is directed towards the use of Lagrangean relaxation. The Multi-objective
problem to which most effort is devoted here is the Maximum Covering
Shortest Path (MCSP) problem. MCSP seeks a path in a network, from starting
(source) node to terminus (sink) node, which is simultaneously as short
as possible and covers the maximum population (by passing within a 'covering
distance'). Our approach differs from the existing one, based on use
of a general integer programming package, using a Lagrangean relaxation
approach instead. The subproblems generated are simple shortest route
problems relative to reduced arc lengths. This avoids the difficulty
of 'isolated circuits' (subtours) encountered previously. On the other
hand, care has to be taken to prevent the occurrence of negative length
circuits (relative to reduced arc lengths). Some experimental results
are presented. Subgradient optimisation is used for the Lagrangean dual
problem. A branch-and bound algorithm is also implemented for closing
any duality gap (which may result from the integrality constraints).
Our approach to MCSP also uses K-shortest path, and a suitable algorithm
for this is devised. The new method called Anticipatory Nemhauser, is
presented together with the data structures used and shown to be very
promising in terms of computation time required. The other problems,
considered briefly, are the Hierarchical Network Design Problem (HNDP)
and the Median Shortest Path Problem (MSPP). For the first of these a
dual-based scheme is developed and applied to an example with considerable
success but further experimentation is required to establish the merits
of our approach more generally. The relationship between MSPP and HNDP
is considered. Finally, the last chapter presents our conclusions and
suggestion for further work.}}
@inproceedings{AggSchTok-SCG-93,
title = {{Finding a minimum weight $K$-link path in graphs with Monge property
and applications}},
author = {Alok Aggarwal and Baruch Schieber and T. Tokuyama},
booktitle = {Proc. 9th Symp. Computational Geometry},
publisher = {ACM},
pages = {189--197},
year = {1993}}
@article{AhuMehOrl-JACM-90,
title = {{Faster algorithms for the shortest path problem}},
author = {Ravindra K. Ahuja and Kurt Mehlhorn and James B. Orlin and Robert
E. Tarjan},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {37},
pages = {213--223},
year = {1990}}
@techreport{AhuMehOrl-TR-88,
title = {{Faster algorithms for the shortest path problem}},
author = {Ravindra K. Ahuja and Kurt Mehlhorn and James B. Orlin and Robert
E. Tarjan},
institution = {MIT Operations Research Ctr.},
number = {193},
year = {1988}}
@article{Aih-ECJ-75,
title = {{An approach to enumerating elementary paths and cutsets by Gaussian
elimination method}},
author = {K. Aihara},
journal = {Electronics and Communications in Japan},
volume = {58},
number = {1},
pages = {1--10},
year = {1975},
abstract = {Discusses a new method of enumerating elementary paths and
cutsets for all node pairs in a graph by means of Gaussian elimination.
Elimination of elementary paths and cutsets is very important from the
viewpoint of graph theory as well as network theory. In the past, the
combinatorial method and the algebraic approach have been discussed independently
although both are impractical.}}
@article{Alt-ICCA-97,
title = {{On the K-best mode in computer chess: measuring the similarity
of move proposals}},
author = {Ingo Alth{\"o}fer},
journal = {ICCA J.},
volume = {20},
number = {3},
pages = {152--165},
month = {September},
year = {1997}}
@techreport{Alt-TR-99,
title = {{Decision Support Systems With Multiple Choice Structure}},
author = {Ingo Alth{\"o}fer},
type = {Jenaer Schriften zur Mathematik und Informatik},
address = {D-07740 Jena, GERMANY},
institution = {Friedrich-Schiller-Univ. Jena, Fakult{\"a}t f{\"u}r Mathematik und
Informatik},
number = {99-31},
month = {June},
year = {1999},
url = {http://www.minet.uni-jena.de/Math-Net/reports/shadows//99-31report.html}}
@article{AltWen-AAM-99,
title = {{Two-best solutions under distance constraints: the model and
exemplary results for matroids}},
author = {Ingo Alth{\"o}fer and Walter Wenzel},
journal = {Advances in Applied Math.},
volume = {22},
number = {2},
pages = {155--185},
month = {February},
year = {1999},
abstract = {In discrete maximization problems one typically wants to find
an optimal solution. However, in topics like ``alignment of DNA-strings,''
``automatic speech recognition,'' and ``computer chess'' people have been
asking for finding not only the best, but the $k$ best solutions. Sometimes
it becomes a problem when these $k$ best solutions are too similar. This
similarity problem may be overcome by demanding that the $k$ solutions
obey certain distance conditions. We investigate the simplest case $k=2$
and we look at valuated matroids. We present several exemplary results,
concerning also time complexity. These results are interesting in themselves.
But they are also good references for similar studies in other fields
with less smooth structures.}}
@techreport{AltWen-TR-97,
title = {{Two-best solutions under distance constraints: the model and
exemplary results for matroids}},
author = {Ingo Alth{\"o}fer and Walter Wenzel},
institution = {Friedrich-Schiller-Universit{\"a}t Jena, Fakult{\"a}t f{\"u}r Mathematik
und Informatik},
number = {Math/Inf/97/17},
month = {20 June},
year = {1997},
abstract = {In discrete maximization problems one typically wants to find
an optimal solution. However, in topics like ``alignment of DNA-strings'',
``automatic speech recognition'', and ``computer chess'' people have been
asking for finding not only the best, but the $k$ best solutions.
Sometimes it becomes a problem when these $k$ best solutions are too
similar. This similarity problem may be overcome by demanding that the
$k$ solutions obey certain distance conditions.
We investigate the simplest case $k=2$ and look at valuated matroids.
We present several exemplary results, concerning also time complexity.
These results are interesting in themselves. But they are also good references
for similar studies in other fields with less smooth structures.}}
@techreport{AltWen-TR-98,
title = {{$k$-best solutions under distance constraints in valuated $\Delta$-matroids}},
author = {Ingo Alth{\"o}fer and Walter Wenzel},
institution = {Friedrich-Schiller-Universit{\"a}t Jena, Fakult{\"a}t f{\"u}r Mathematik
und Informatik},
number = {Math/Inf/98/14},
month = {27 May},
year = {1998},
abstract = {In discrete maximization problems one usually wants to find
an optimal solution. However, in several topics like ``alignments'', ``automatic
speech recognition'', and ``computer chess'' people are interested to find
the $k$ best solutions for some $k\ge 2$. We demand that the $k$ solutions
obey certain distance constraints to avoid that the $k$ alternatives
are too similar. Several results for valuated $\Delta$-matroids are presented,
and we concern in particular time complexity.}}
@inproceedings{AmiGha-IPEC-93,
title = {{An expert system for transmission line route selection}},
author = {El-Amin and Al-Ghamdi},
booktitle = {Int. Power Engineering Conf},
publisher = {Nanyang Technol. Univ, Singapore},
volume = {2},
pages = {697--702},
year = {1993},
abstract = {An expert system (ES) is developed to help power system planners
to choose the 'most suitable' transmission line route. The 'most suitable'
route is the one that minimizes disruption to the surrounding environment
as well as meeting any social constraints. The electric utility will
tentatively identify up to five possible routes based on cost only. These
routes are identified by the K-shortest path method. The chosen routes
are then subjected to environmental and social factor using the developed
ES. Factors such as crossing existing lines, running parallel to existing
line, crossing crude oil pipelines etc. are considered. The ES assigns
a cost value and weight for each factor and then normalizes the overall
weight. The route with the lowest disruption is chosen. The ES was tested
on a 69 kV distribution system for connecting two substations. The results
obtained are in full agreement with the results obtained when complex
integer goal programming (IGP) are used. They also conform with what
the electric utility engineers expected.}}
@techreport{AmTsuShi-TR-76,
title = {{An algorithm for generating all the paths between two vertices
in a digraph and its application}},
author = {T. D. Am and S. Tsukiyama and I. Shirakawa and H. Ozaki},
institution = {Osaka Univ.},
year = {1976},
abstract = {An algorithm to generate all the directed paths from a specified
vertex to another one in a given directed graph is proposed. The algorithm
requires the processing time bounded by the order $O((n+m)(p+1))$ and
the memory space bounded by $O(n+m)$, where $n$, $m$, and $p$ denote
the number of vertices, edges, and directed paths in a given directed
graph, respectively. As an application of the algorithm, the shortest
or the longest path problem in a directed graph containing cycles of
negative weight is also considered.}}
@inproceedings{AnaSchShu-ASSP-95,
title = {{Duration modeling in large vocabulary speech recognition}},
author = {A. Anastasakos and Richard Schwartz and Han Shu},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {628--631},
month = {May},
year = {1995},
abstract = {This paper presents a study of different methods for phoneme
duration modeling in large vocabulary speech recognition. We investigate
the employment of phoneme duration and the effect of context, speaking
rate and lexical stress in the duration of phoneme segments in a large
vocabulary speech recognition system. The duration models are used in
a postprocessing phase of BYBLOS, our baseline HMM-based recognition
system, to rescore the $N$-Best hypotheses. We describe experiments with
the 5 K word ARPA Wall Street Journal (WSJ) corpus. The results show
that integration of duration models that take into account context and
speaking rate can improve the word accuracy of the baseline recognition
system.}}
@article{AniHas-SJC-89,
title = {{Ranking the best binary trees}},
author = {S. Anily and Refael Hassin},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {18},
pages = {882--892},
year = {1989},
review = {MR-91d-68098}}
@article{MR-91d-68098,
reviews = {AniHas-SJC-89},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Ranking the best binary trees}},
volume = {91d},
number = {68098},
year = {1991},
text = {The problem of ranking the $K$-best binary trees with respect to
their weighted average leaves' levels is considered. Both the alphabetic
case, where the order of the weights in the sequence $w\sb 1,\cdots,w\sb
n$ must be preserved in the leaves of the tree, and the nonalphabetic
case, where no such restriction is imposed, are studied. For the alphabetic
case a simple algorithm is provided for ranking the $K$-best trees, based
on a recursive formula of complexity $O(Kn\sp 3)$. For nonalphabetic
trees two different ranking problems are considered, and for each of
them it is shown that the next best tree can be solved by a dynamic programming
formula of low complexity order.}}
@inproceedings{ArdMal-ACCS-71,
title = {{A recursive algorithm for generating circuits and related subgraphs}},
author = {M. T. Ardon and N. R. Malik},
booktitle = {Proc. 5th Asilomar Conf. Circuits {\&} Systems},
publisher = {Western Periodicals Co.},
editor = {S. R. Parker},
pages = {279--284},
year = {1972},
abstract = {A technique is proposed for efficiently finding the set of
all or some specified sets of circuits, paths, directed circuits and
directed paths of a directed graph. The method employs the matrix defined
by $M=C+I$, where $C$ is the variable adjacency matrix of the graph,
and $I$ is an identity matrix. The method is an extension of Lempel and
Cederbaum's (1966) procedure. By their technique the directed circuits
are found by applying the Boolean reduction to an expression which is
resulted from the permanent expansion of $M$. Here, a new expansion,
the pseudo-permanent, is defined by which the set of directed circuits
is found directly. The procedure is then modified to obtain particular
sets of directed circuits and an arbitrarily specified set of directed
paths. An extension to nonoriented graphs results in an efficient algorithm
for generating undirected circuits.}}
@article{AriTsuShi-IEICE-79,
title = {{Algorithms for enumerating all the $s$-$t$ cutsets in $O(|V|+|E|)$
per cutset}},
author = {H. Ariyoshi and S. Tsukiyama and I. Shirakawa and H. Ozaki},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E62},
number = {1},
pages = {22--23},
month = {January},
year = {1979},
abstract = {Presents two algorithms with time complexity of $O((n+m)(\nu+1))$;
one has space complexity of $O(n^2)$ and the other of $O(n+m)$, where
$n$, $m$, and $\nu$ are the numbers of vertices, edges, and $s$-$t$ cutsets
in a graph, respectively.}}
@inproceedings{AsaSat-GTA-84,
title = {{Long path enumeration algorithms for timing verification on large
digital systems}},
author = {Tetsuo Asano and Shinichi Sato},
booktitle = {Graph Theory with Applications to Algorithms and Computer
Science},
publisher = {Wiley-Interscience},
pages = {25--35},
year = {1984},
review = {MR-87b-94065}}
@article{MR-87b-94065,
reviews = {AsaSat-GTA-84},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Long path enumeration algorithms for timing verification on large
digital systems}},
volume = {87b},
number = {94065},
year = {1987},
text = {To insure that a digital system will operate at a desired speed,
the designer must verify that every path delay is not too long or too
short. Thus, an efficient path enumeration technique is needed. In this
paper we present two algorithms for enumerating all possible paths in
a directed acyclic graph that exceed given delay time. They run in $O(m\log
m+N(K))$ and $O(Km)$ time, respectively, and require $O(m+n)$ space,
where $K,m$, and $n$ are the number of such long paths, arcs, and nodes
of a graph, and $N(K)$ is the total number of nodes on $K$ such long
paths.}}
@article{Awa-IJPR-87,
title = {{A counter-example to Naidu-Singh's myopic algorithm for generation
of Wagner-Whitin optimal ordering plan (lot sizing)}},
author = {P. G. Awate},
journal = {Int. J. Production Res.},
volume = {25},
number = {8},
pages = {1235--1237},
month = {August},
year = {1987},
abstract = {The paper gives a simple counter-example to the conjecture
by Naidu and Singh (see ibid., vol.24, no.1, p.223 (1986)) that their
algorithm 'gives the optimal solution like the W-W algorithm'. Secondly,
it points out that the Naidu-Singh procedure attempts to find the cheapest
path in a certain acyclic network whose nodes are sets of periods and
where the kth cheapest path does not necessarily have any node in common
with 2nd or 3rd or. . .or (k-1)st-cheapest path.}}
@article{AweBerCow-SJC-98,
title = {{Near-linear time construction of sparse neighborhood covers}},
author = {Baruch Awerbuch and Bonnie Berger and Lenore Cowen and David
Peleg},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {28},
number = {1},
pages = {263--277},
year = {1998},
comment = {Despite the reference in the abstract to k-shortest-paths, what
they actually approximate is the set of shortest paths for k source-destination
pairs. Obviously this can be solved by k applications of Dijkstra in
O(k(m+n log n)) time but they achieve a linear time approximation.},
abstract = {This paper introduces a near-linear time sequential algorithm
for constructing a sparse neighborhood cover. This implies analogous
improvements (from quadratic to near-linear time) for any problem whose
solution relies on network decompositions, including small edge cuts
in planar graphs, approximate shortest paths, and weight- and distance-preserving
graph spanners. In particular, an O(log n) approximation to the k-shortest
paths problem on an n-vertex, E-edge graph is obtained that runs in O(n+E+k)
time.}}
@article{AyaCab-DACS-92,
title = {{Path enumeration and hot-potato routing analysis in multihop
networks}},
author = {E. Ayanoglu and R. J. Caballero},
journal = {Int. J. Digital and Analog Communication Systems},
volume = {5},
pages = {217--223},
year = {1992},
abstract = {Using labelling of the edges of the network graph for a multihop
network (using deflection routeing) and a Taylor series expansion of
the transfer function of the resulting signal flow graph, the authors
calculate the number of paths of a given length in the multihop network.
The derivative of the transfer function and a fixed point algorithm yield
the average delay as a function of the packet arrival rate.}}
@article{AzeSanSil-EJOR-93,
title = {{An algorithm for the ranking of shortest paths}},
author = {J. A. Azevedo and Santos Costa, M. E. O. and Silvestre Madeira,
J. J. E. R. and Ernesto de Queir{\'o}s Vieira Martins},
journal = {Eur. J. Operational Research},
volume = {69},
pages = {97--106},
year = {1993},
abstract = {An efficient computational implementation of a path deletion
$K$ shortest paths algorithm and a new algorithm for the same problem
are presented. In a path deletion $K$ shortest paths algorithm a sequence
$(G_1, G_2, \ldots, G_k)$ of networks is defined, such that $G_1$ is
the given network and its $k$-th shortest path is trivially determined
from the shortest path in $G_k$. In essence, as soon as the shortest
path in $G_k$ is determined it is excluded from $G_k$ in such a way that
no new paths are formed and no more paths are deleted. So, for each $G_k$,
two procedures are executed: a shortest path algorithm and a path deletion
algorithm. In the presented computational implementation, all the information
resulting from the determination of the $k$-th shortest path is carried
throughout $G_k+1, G_k+2, \ldots, G_k$. The new algorithm not only keeps
this characteristic but also avoids the last $K-1$ executions of a shortest
path algorithm, which results in a surprising and very substantial reduction
in the execution time. In fact, for randomly generated networks with
$10^4$ nodes and $10^5$ arcs, once the shortest path is determined, the
new algorithm computes the next $100$ shortest paths in times of the
order of $10^{-1}$ seconds. To illustrate the efficiency of this algorithm,
comparative computational experiments are reported.}}
@inproceedings{AzeSilMar-AIRO-90,
title = {{A shortest paths ranking algorithm}},
author = {J. A. Azevedo and Silvestre Madeira, J. J. E. R. and Ernesto
de Queir{\'o}s Vieira Martins and F. M. A. Pires},
booktitle = {Proc. AIRO 1990},
publisher = {Associazione Italiana Ricerca Operativa},
pages = {1001--1011},
year = {1990},
url = {http://www.mat.uc.pt/~eqvm/cientificos/investigacao/r_papers.html},
abstract = {The ranking of K shortest paths is a classical network optimization
problem with a large range of real world applications. Take as an example
the constrained shortest path problem, where some complex set of constraints
is associated with each path. If these constraints are ignored and paths
are listed by increasing order of objective values, the shortest path
verifying the given set of constraints is thus determined.
The shortest path ranking problem may also occur in the multiobjective
shortest path problem. In fact, a procedure for determining the multiobjective
shortest path involves the knowledge of a well defined set of paths,
namely the set of nondominated paths, which can be computed by a shortest
paths ranking algorithm.
For the ranking of shortest paths (loopless or not) problem, there are
three classes of algorithms. One of them is based on the {\it Principle
of Optimality}, being Dreyfus' algorithm its most representative one.
Another classe comprises the generalizations, due to Shier, of labeling
shortest paths algorithms. Finally, the last class encompasses the algorithms
based on the path deletion concept, due to one of the authors.
A new algorithm belonging to this class is presented. We prove that,
in a worst case analysis, its executation time is as good as that of
Dreyfus' algorithm that, as far as we know, has been considered the best
algorithm for the problem.
Computational experiments showing its clearly better performance are
also presented. As an example, we report tests on random networks with
1500 nodes and 15000 arcs where the new algorithm to determine 250 paths
was about 60 times faster than Dreyfus' algorithm.}}
@article{AzeSilMar-EJOR-94,
title = {{A computational improvement for a shortest paths ranking algorithm}},
author = {J. A. Azevedo and Silvestre Madeira, J. J. E. R. and Ernesto
de Queir{\'o}s Vieira Martins and F. M. A. Pires},
journal = {Eur. J. Operational Research},
volume = {73},
pages = {188--191},
year = {1994},
abstract = {Presents a computational improvement for the shortest paths
ranking algorithm due to some of the authors. According to its computational
complexity, this new version of the algorithm entails a very significant
reduction in its execution time and an even larger reduction in the required
computer memory space. Computational experiments are reported.}}
@article{AziSobSam-MR-94,
title = {{Fast enumeration of every path in a reliability graph using subgraphs}},
author = {M. A. Aziz and M. A. Sobhan and M. A. Samad},
journal = {Microelectronics and Reliability},
volume = {34},
pages = {1395--1396},
year = {1994},
abstract = {A fast method has been proposed for enumeration of all possible
pathsets from every node to all other nodes using subgraphs. The method
efficiently identifies the elements as well as source, sink and other
nodes constituting a path. It performs no multiplications other than
a few additions of binary digits.}}
@article{BaaAshAnw-Tr-96,
title = {{Transportation analysis for sludge landfill site selection --
a case study demonstration}},
author = {M. H. Baaj and S. Ashur and A. Anwar},
journal = {Transportation},
volume = {23},
number = {2},
pages = {191--209},
month = {May},
year = {1996},
note = {A solution framework for the Sludge Landfill Site Selection Problem
(SLSSP) which arises in the context of environmental planning is presented.
The problem may be defined as follows: given a set of environmentally
acceptable candidate landfill sites, identify the site which minimizes
a weighted combination of two objectives (system descriptors): the present
worth value of the transportation operation costs and the resulting population
disturbance of the chosen set of transportation routes. The solution
framework relies on an analysis algorithm which identifies K shortest
travel time routes between one candidate landfill site and each of the
water treatment plants. Based on a prespecified tradeoff between present
worth and population disturbance, the transportation routes associated
with each landfill site are selected and the site's two resulting system
descriptors are computed. The solution methodology is demonstrated on
data developed for the City of Phoenix, Arizona. In addition, computational
experiments are performed to rest the quality of solution and its sensitivity
to different tradeoffs between the two system descriptors. As a result
of this study, city officials were dissuaded away from a prefavored landfill
site. Final selection from the set of pareto-optimal solutions was postponed
pending results of ongoing efforts
to enlarge the collection operation by including sludge disposed in other
neighboring cities.}}
@article{BabFunNis-IEICE-98,
title = {{A proposal of a greedy neural network for route assignments in
multihop radio networks}},
author = {T. Baba and N. Funabiki and S. Nishikawa},
journal = {Trans. IEICE},
volume = {J81D-I},
number = {6},
pages = {700--707},
month = {June},
year = {1998},
abstract = {In a multihop radio network, packets are transmitted from source
nodes to destination nodes by activating several links between nodes.
Each node can either send a packet to, or receive a packet from, almost
one of its adjacent nodes simultaneously. In order to minimize the transmission
time for given requests, the route assignment problem must be solved
to assign a transmission route for each request, and the link activation
problem must be solved to find a link activation schedule. The route
assignment problem is decomposed into two sub-problems: the candidate
extraction problem and the route selection problem. We propose a cost
function for the route assignment problem and secondly, we propose the
k-shortest route extraction method for the candidate extraction problem.
This method is based on the k-shortest path algorithm, and extracts only
routes whose number of hops is limited by the largest length among the
shortest routes for all the SD pairs without loops and redundant nodes.
The number of different extracted candidates is also limited by the minimum
number of hops for each request. Thirdly, we propose the greedy neural
network algorithm for the route selection problem. The greedy neural
network consists of the greedy initialization method with the number
of hops of the corresponding candidate, the motion equation with the
w function and the new term of minimizing the cost function, and the
one dimensional maximum neutron model. Through simulations in up to 500-node
networks, we verify that our algorithm finds better solutions in shorter
time with smaller space than the existing algorithms.}}
@article{BabFunNis-SCJ-99,
title = {{A proposal of a greedy neural network for route assignments in
multihop radio networks}},
author = {T. Baba and N. Funabiki and S. Nishikawa},
journal = {Systems and Computers in Japan},
volume = {30},
number = {13},
pages = {52--60},
month = {November},
year = {1999}}
@article{Bak-MOS-76,
title = {{All paths in an activity network}},
author = {A. Bako},
journal = {Mathematische Operationsforschung und Statistik},
volume = {7},
pages = {851--858},
year = {1976},
abstract = {The known CPM/PERT methods are available for the determination
of the critical edges and a critical path. This paper gives two algorithms:
one of them is used for the determination of all critical paths, the
second for the determination of the second longest paths. The validity
of the algorithms and the labelling technique are also given.}}
@article{BakKas-Sz-77,
title = {{Determining the $k$-th shortest path by matrix method}},
author = {A. Bako and P. Kas},
journal = {Szigma},
volume = {10},
pages = {61--66},
year = {1977},
abstract = {An algorithm is given for the multiterminal version of the
$k$-th shortest path problem. The algorithm calculates in n steps the
length of the first $k$ paths between all the point pairs of a digraph.
The labelling technique required for the determination of the paths and
the procedure supplying the intermediate points belonging to the path
are described. Altogether the calculation consists of $kn^3$ additions
and $k^3/2 n^3$ [Note - this formula was garbled, I have attempted to
reconstruct it but may have erred - DE] comparisons. This number is considerably
lower than what is necessary for the repeated application of the $k$-th
shortest path algorithm of two end points known in literature.},
note = {In Hungarian}}
@phdthesis{Bal-PhD-87,
title = {{A Network Model for Rotating Workforce Scheduling and Related
Problems}},
author = {Nagraj Balakrishnan},
school = {Purdue Univ., Dept. of Business Administration},
year = {1987},
abstract = {The rotating workforce scheduling problem, which is an important
factor in improving worker productivity, involves the construction of
an efficient sequence of work and recreation periods spanning over a
number of weeks. This schedule must satisfy the workforce requirements
during the various time periods and conform to all the other conditions
imposed on the work/recreation periods and their sequence. We consider
the modelling of the rotating workforce scheduling problem as a network
flow problem. All the conditions enforced on the problem are incorporated
in the network itself, except for the staff-covering constraints which
are treated as side constraints. The optimal solution to the problem
is a path in the network and is identified using a dual-based approach.
The model deals with the three issues of recreation period identification,
work/recreation period sequencing and shift scheduling simultaneously,
and is designed to handle multiple shifts with time varying demands.
A software package which includes the network model along with the solution
technique is developed. To illustrate its use, the procedure, which is
capable of solving large-scale problems, is applied to three well-known
problems in rotating workforce scheduling. The computational results
presented indicate that this procedure provides us with a useful method
of solving large-scale complex problems in workforce scheduling. The
general model developed can also be applied to other problems in sequencing
and scheduling. To illustrate this feature, we consider a particular
aspect of the examination timetabling problem where the objective is
to assign blocks of examinations to time periods such that the number
of students having back-to-back conflicts is minimized. The time periods
are defined in such a way that the last period of any day and the first
period of the following day are not considered to be back-to-back. The
problem is modelled as a network flow problem where the solution to the
problem is the shortest path in the network subject to side-constraints.
A dual based approach followed by a K-shortest path enumeration technique
is employed to identify this optimal path. The procedure is tested on
a variety of test problems including a real problem faced by a large
university.}}
@article{BalDerHil-Nw-90,
title = {{Matching problems with generalized upper bound side constraints}},
author = {Michael O. Ball and Ulrich Derigs and C. Hilbrand and Achim Metz},
journal = {Networks},
volume = {20},
number = {6},
pages = {703--721},
year = {1990},
review = {MR-91h-90068}}
@article{MR-91h-90068,
reviews = {BalDerHil-Nw-90},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Matching problems with generalized upper bound side constraints}},
author = {Frank Werner},
volume = {91h},
number = {90068},
year = {1991},
text = {The paper considers procedures for the approximate solution of
matching problems with generalized upper bound side constraints which
are based on Lagrangian relaxation and dual ascent. In the first phase
the standard Langrangian relaxation ideas are used to determine lower
bounds for matching problems with side constraints. In the second phase
an improvement technique is applied to the subsequences of feasible and
infeasible matchings obtained in phase one. Namely, a knapsack heuristic
is applied to any pair of feasible/infeasible matchings to construct
better feasible matchings. If the optimal solution is desired, then an
enumeration phase, in which a sequence of $k$-best matchings with respect
to a penalized objective function is constructed, can be added. Finally,
computational results are presented for a set of test problems with one
and five constraints.}}
@inproceedings{BalSte-AFCT-91,
title = {{Topologies for linear lightwave networks}},
author = {K. Bala and T. E. Stern},
booktitle = {Advanced Fiber Communications Technologies},
number = {1579},
series = {Proc. SPIE},
publisher = {Int. Soc. Optical Engineering},
pages = {62--73},
year = {1991},
abstract = {Tree based networks which preclude the possibility of certain
violations are compared with networks that allow violations but achieve
better load distribution. The performance of each topology, from the
point of view of blocking probability is compared by a simulator using
call routing based on the $K$-shortest path algorithm. It is found that
general topologies that allow for better load distribution perform better
than tree based topologies.}}
@inproceedings{BalSteBal-INFOCOM-91,
title = {{Algorithms for routing in a linear lightwave network}},
author = {K. Bala and T. E. Stern and K. Bala},
booktitle = {Proc. 10th Joint. Conf. IEEE Computer {\&} Communications Socs.},
volume = {1},
pages = {1--9},
year = {1991},
abstract = {Routing algorithms are proposed for setting up calls on a circuit-switched
basis in linear lightwave networks (LLN), i.e., networks composed only
of linear components, including controllable power combiners and dividers,
and possibly linear (non-regenerative) optical amplifiers. The overall
problem is decomposed into three subproblems: (1) physical path allocation,
(2) checking for violations of the special optical constraints on the
allocated physical path, and (3) channel assignment. Only point to point
connections are considered. The physical path allocation technique uses
the K-shortest path algorithm and tries to minimize the number of sources
potentially interfering with each other, as a result of the incoming
call. A channel assignment heuristic that tends to spread out calls evenly
among the available channels works better than one that tries to maximize
channel reuse.}}
@article{BalSteSim-TN-95,
title = {{Routing in a linear lightwave network}},
author = {K. Bala and T. E. Stern and D. Simchi-Levi and K. Bala},
journal = {Trans. on Networking},
publisher = {IEEE and ACM},
volume = {3},
number = {4},
pages = {459--469},
month = {August},
year = {1995},
abstract = {Dynamic routing of point-to-point connections in a waveband
selective linear lightwave network is addressed. Linear lightwave networks
are all optical networks in which only linear operations are performed
on signals in a waveband selective manner. Special constraints arise
because of the linearity in the linear lightwave network. The overall
problem of finding a path satisfying all the routing constraints for
point-to-point connections is shown to be very complex. Owing to the
complexity, the overall routing problem is decomposed into several subproblems.
In particular, given a request for a point-to-point connection a waveband
is first chosen for the call. Two heuristics, MAXBAND which allocates
the most used band to a call and another MINBAND (least used band) are
studied. Then, the problem of routing in a given waveband is further
divided into smaller subproblems of finding a path in the waveband, checking
for feasibility of the path in the chosen waveband and channel allocation
(within the waveband). For finding paths in a waveband, K-SP, BLOW-UP
and MIN-INT algorithms are proposed. A recursive algorithm checks for
feasibility of the path on the waveband. Two channel allocation schemes
(within a single waveband) MIN and MAX are presented. Simulations show
that using MAXBAND (waveband), MIN-INT (path on waveband) and MIN (channel
within waveband) policies resulted in the best performance (least blocking).}}
@phdthesis{Bar-PhD-95,
title = {{A Quasi-Static Routing Optimization Model for Telecommunication
Networks}},
author = {Michael Raymond Bartolacci},
school = {LeHigh Univ., Dept. of Industrial Engineering},
year = {1995},
abstract = {The main focus of this research is the development of a routing
optimization model for telecommunication networks that utilizes nodal
clustering as a 'preprocessor' to routing. The routing model developed
contains three submodels: the clustering submodel (CLUS), the inter-cluster
routing submodel (INTER), and the intra-cluster routing submodel (INTRA).
The clustering problem is solved through a modified version of 'problem
space' search, while inter-cluster and intra-cluster routing is conducted
in a dynamic manner. This clustered routing method out-performed a standard
dynamic routing algorithm and a static approach with respect to minimizing
average source-to-destination routing delay. A secondary focus of this
research is the generation of test problem sets for telecommunication
network routing. A procedure is developed which generates topologies
with random geometric structures. A set of test problems based on PREPNET,
a mid-level network on the NSFnet backbone, are also developed. A third
focus of this research is a static, k shortest path-based, approach for
bifurcated and single path routing in telecommunication networks. This
proposed routing method is tested against a single path routing algorithm
for a variety of network topologies and traffic requirements.}}
@techreport{BarKhuSch-TR-95,
title = {{The complexity of finding most vital arcs and nodes}},
author = {Amotz Bar-Noy and Samir Khuller and Baruch Schieber},
organization = {Univ. of Maryland, Dept. of Computer Science},
number = {CS-TR-3539},
month = {November},
year = {1995},
url = {ftp://ftp.cs.umd.edu/pub/papers/papers/3539/3539.ps.Z},
abstract = {Let $G(V,E)$ be a graph (either directed or undirected) with
a non-negative length $\ell(e)$ associated with each arc e in E. For
two specified nodes s and t in V, the k most vital arcs (or nodes) are
those k arcs (nodes) whose removal maximizes the increase in the length
of the shortest path from s to t. We prove that finding the k most vital
arcs (or nodes) is NP-hard, even when all arcs have unit length. We also
correct some errors in an earlier paper by Malik, Mittal and Gupta \cite{MalMitGup-ORL-89}.}}
@article{BarZie-SMC-91,
title = {{Topological analysis of satellite-based distributed sensor networks}},
author = {Craig M. Barnhart and R. E. Ziemer},
journal = {Trans. Systems, Man, and Cybernetics},
publisher = {IEEE},
volume = {21},
number = {5},
pages = {1060--1070},
year = {1991},
abstract = {A method for evaluating the topological quality of networks
for distributed sensor applications is presented. The criteria for evaluation
are network survivability and delay. Nodal connectivity is used to characterize
survivability, and mean path length is used to characterize delay. To
calculate these two quantities, an algorithm is developed to find k shortest
node-disjoint paths between a pair of nodes when each link has unit distance.
As an example of the use of this type of analysis, the effects of nodal
losses in a multiple-node satellite network consisting of a Walker low-orbit
sphere and a geosynchronous constellation are examined. The example
demonstrates how topological analysis on the basis of connectivity and
mean path length may be used to detect, and subsequently address, potential
flaws in a network design. The results show that the geosynchronous/low-orbit
link assignment protocol should be a primary concern in the design of
this network. They also show that the nodal degree of the failed node,
and the distribution of links between the Walker sphere and the geosynchronous
constellation, are the fundamental determinants of mean path length.}}
@article{Bax-IPL-94,
title = {{Algorithms to count paths and cycles}},
author = {Eric Theodore Bax},
journal = {Information Processing Letters},
volume = {52},
number = {5},
pages = {249--252},
month = {December},
year = {1994},
abstract = {We use results for Hamiltonian cycles and paths to deduce $O(2^n{\rm
poly}(n))$ time and $O({\rm poly}(n))$ space algorithms to count: (1)
cycles on a single vertex, (2) all cycles, (3) paths between a given
pair of vertices, and (4) all paths in a graph with $n$ vertices.},
review = {MR-95h-68072}}
@article{MR-95h-68072,
reviews = {Bax-IPL-94},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Algorithms to count paths and cycles}},
volume = {95h},
number = {68072},
year = {1995}}
@phdthesis{Bax-PhD-98,
title = {{Finite-Difference Algorithms for Counting Problems}},
author = {Eric Theodore Bax},
school = {California Inst. of Technology, Dept. of Computer Science},
year = {1998},
abstract = {We present a novel method to construct counting algorithms:
(1) Construct a generating function in which one type of terms corresponds
to the objects to be counted. (2) Apply the proper finite-difference
operators to produce a formula that counts the terms. (3) Choose finite-difference
parameters to reduce the computation required to evaluate the formula.
We compare this finite-difference method to two other methods, the dynamic
programming method and the inclusion and exclusion method. Using the
problem of counting Hamiltonian paths as an example, we show that finite-difference
algorithms require only polynomial space for problems for which dynamic
programming algorithms require exponential space. Also, we show that
finite-difference algorithms are a generalization of inclusion and exclusion
algorithms. Finite-difference algorithms have some free parameters, and
inclusion and exclusion algorithms correspond to a particular setting
of those parameters. Using the 0-1 matrix permanent problem as an example,
we show that the finite-difference parameters can be chosen to produce
finite-difference algorithms that are faster than their inclusion and
exclusion counterparts. We use the problems of counting paths by length
and counting independent path sets to illustrate how the flexibility
of generating functions and extensions to finite-difference operators
allow the development of finite-difference algorithms for problems beyond
the realm of inclusion and exclusion. Furthermore, we use the problems
of sequencing, bin packing, and deadlock avoidance to demonstrate the
development of finite-difference algorithms for NP-complete and {\#}P-complete
problems.}}
@article{Bei-Comp-72,
title = {{An algorithm for finding all $k$-shortest distances in a network}},
author = {H. Beilner},
journal = {Computing},
volume = {10},
pages = {205--220},
year = {1972},
abstract = {This paper describes a new matrix-algorithm for determining
all shortest up to $k$-shortest distances between the $n$ vertices of
a network. The outstanding property of this algorithm consists in the
necessary amount of additions/subtractions which can be estimated, for
$n\gg k$, not to exceed $1/3 n^5/2 k^5/2 + 5 n^5/2 k^3/2 + O(n^3/2 k^5/2)$
whereas the number of comparisons lies, as in other algorithms, in the
range of $n^3 k^3$. This paper also includes a formal proof of the validity
of the algorithm and a short comparison with different, known methods.},
note = {In German}}
@article{Bel-QAM-58,
title = {{On a routing problem}},
author = {Richard E. Bellman},
journal = {Quarterly of Applied Mathematics},
volume = {16},
number = {1},
pages = {87--90},
year = {1958}}
@article{BelKal-SIAM-60,
title = {{On $k$th best policies}},
author = {Richard E. Bellman and R. Kalaba},
journal = {J. SIAM},
publisher = {SIAM},
volume = {8},
pages = {582--588},
year = {1960},
review = {MR-22-13305}}
@article{MR-22-13305,
reviews = {BelKal-SIAM-60},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On $k$th best policies}},
author = {T. E. Hull},
volume = {22},
number = {{\#}13305},
year = {1961}}
@article{BerGenPot-JH-00,
title = {{Tabu search for a network loading problem with multiple facilities}},
author = {D. Berger and B. Gendron and J.-Y. Potvin and S. Raghavan and
P. Soriano},
journal = {J. Heuristics},
volume = {6},
number = {2},
pages = {253--267},
month = {June},
year = {2000},
abstract = {Examines a network design problem that arises in the telecommunications
industry. In this problem, communication between a gateway vertex and
a number of demand vertices is achieved through a network of fiber-optic
cables. Since each cable has an associated capacity (bandwidth), enough
capacity must be installed on the links of the network to satisfy the
demand, possibly using different types of cables. Starting with a network
with no capacity or some capacity already installed, a tabu search heuristic
is designed to find a solution that minimizes the cost of installing
any additional capacity on the network. This tabu search applies a k-shortest
path algorithm to find alternative paths from the gateway to the demand
vertices. Numerical results are presented on different types of networks
with up to 200 vertices and 100 demand vertices.}}
@inproceedings{BesKel-AWOCA-99,
title = {{Algorithms for shortest paths and $d$-cycle problems}},
author = {Sergei Bespamyatnikh and Andrei Kelarev},
booktitle = {Proc. 10th Aust. Worksh. Combinatorial Algorithms},
pages = {152--156},
year = {1999},
url = {http://www.cs.ubc.ca/~besp/cycle.ps.gz},
abstract = {Let $G$ be a weighted graph with $n$ vertices and $m$ edges.
We address the $d$-cycle problem, i.e., the problem of finding a subgraph
of minimum weight with given cyclomatic number $d$. Hartvigsen [5] presented
an algorithm with running time $O(n^2 m)$ and $O(n^{2d-1} m^2)$ for the
cyclomatic numbers $d=1$ and $d\ge 2$, respectively. Using a $(d+1)$-shortest-paths
algorithm, we develop a new more efficient algorithm for the $d$-cycle
problem with running time $O(n^{2d-1} + n^2 m+ n^3\log n)$.}}
@inproceedings{BetHil-ASSP-95,
title = {{Language models for a spelled letter recognizer}},
author = {M. Betz and H. Hild},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {856--859},
month = {May},
year = {1995},
abstract = {In some speech recognition applications, it is reasonable to
constrain the search space of a speech recognizer to a large but finite
set of sentences. We demonstrate the problem on a spelling task, where
the recognition of continuously spelled last names is constrained to
110000 entries (=43000 unique names) of a telephone book. Several techniques
to address this problem are compared: recognition without any language
model, bigrams, functions to map a hypothesis onto a legal string, $n$-best
lists, and finally a newly developed method which integrates all constraints
directly into the search process within reasonable memory and time bounds.
The baseline result of 56{\%} string accuracy is improved to 62, 85, 88,
and 92{\%}, respectively.}}
@article{BilEll-JPDC-95,
title = {{An algorithm for finding the $K$-best allocations of a tree structured
program}},
author = {A. Billionnet and S. Elloumi},
journal = {J. Parallel and Distributed Computing},
volume = {26},
pages = {225--232},
year = {1995},
abstract = {We consider the problem of allocating $n$ tasks of a distributed
program to $m$ processors of a distributed system in order to minimize
total communication and processing costs. If the intertask communication
can be represented by a tree and if the communication costs are uniform,
it is known that an optimal allocation can be determined in $O(nm)$ time.
A $K$-optimal solution set $\Omega=(A_1,\ldots,A_K)$ of a given task
allocation problem is a set of allocations such that no allocation $A$
which is not contained in $\Omega$ is better than any $A_i$, $i=1,\ldots,K$.
In this paper, an algorithm is presented which computes a $K$-optimal
set for the considered task allocation problem in $O(Knm)$.}}
@article{Bof-RAIRO-93,
title = {{The all-to-all alternative route problem}},
author = {Brian Boffey},
journal = {Revue Francaise d'Automatique Informatique Recherche Operationelle
(RAIRO)},
volume = {27},
pages = {375--387},
year = {1993},
review = {MR-94h-90061}}
@article{MR-94h-90061,
reviews = {Bof-RAIRO-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{The all-to-all alternative route problem}},
volume = {94h},
number = {90061},
year = {1994},
text = {There are various $K$-best route problems associated with a network.
The one studied here is that of finding, for all node pairs $(s,t)$,
a best route from $s$ to $t$ together with an alternative route which
is optimal subject to not containing the first edge of the best route.
The relevance of this problem to dynamic vehicle guidance and to routing
in communication networks is briefly discussed. An algorithm is developed
whose complexity, under conditions likely to be met in practice, is established.
An illustrative
example is given.}}
@article{BooWes-Algo-94,
title = {{A linear algorithm for analysis of minimum spanning and shortest-path
trees of planar graphs}},
author = {Heather Booth and Jeffery Westbrook},
journal = {Algorithmica},
volume = {11},
number = {4},
pages = {341--352},
month = {April},
year = {1994},
abstract = {We give a linear time and space algorithm for analyzing trees
in planar graphs. The algorithm can be used to analyze the sensitivity
of a minimum spanning tree to changes in edge costs, to find its replacement
edges, and to verify its minimality. It can also be used to analyze the
sensitivity of a single-source shortest-path tree to changes in edge
costs, and to analyze the sensitivity of a minimum-cost network flow.
The algorithm is simple and practical. It uses the properties of a planar
embedding, combined with a heap-ordered queue data structure.}}
@inproceedings{BraSin-PEW-95,
title = {{A comparative study of $k$-shortest path algorithms}},
author = {A. W. Brander and Mark C. Sinclair},
booktitle = {Proc. 11th UK Performance Engineering Worksh. for Computer
and Telecommunications Systems},
month = {September},
year = {1995},
url = {http://esewww.essex.ac.uk/~mcs/ps/ukpew11_bra.ps.gz},
abstract = {Efficient management of networks requires that the shortest
route from one point (node) to another is known; this is termed the shortest
path. It is often necessary to be able to determine alternative routes
through the network, in case any part of the shortest path is damaged
or busy. The k-shortest paths represent an ordered list of the alternative
routes available. Four algorithms were selected for more detailed study
from over seventy papers written on this subject since the 1950s. These
four were implemented in the `C' programming language and, on the basis
of the results, an assessment was made of their relative performance.}}
@techreport{Bro-RR-126,
title = {{The 1993 SRC Algorithm Animation Festival}},
author = {Marc H. Brown},
type = {SRC Research Report},
institution = {Digital Equipment Corp.},
number = {126},
month = {29 July},
year = {1994},
url = {http://gatekeeper.dec.com/pub/DEC/SRC/research-reports/abstracts/src-rr-126.html}}
@article{BruGhiImp-EJOR-98,
title = {{A multi-modal approach to the location of a rapid transit line}},
author = {G. Bruno and G. Ghiani and G. Improta},
journal = {Eur. J. Operational Research},
volume = {104},
number = {2},
pages = {321--332},
month = {January},
year = {1998},
abstract = {The location of a rapid transit line (RTL) represents a very
complex decision problem because of the large number of decision makers,
unquantifiable criteria and uncertain data. In this context operational
research can help in the design process by providing tools to generate
and assess alternative solutions. For this purpose two bicriterion mathematical
programming models-the maximum coverage shortest path model and the median
shortest path model-have been developed in the past. In this paper a
new bicriterion model, which can evaluate in a more realistic way the
attractivity of an RTL is introduced. To calculate an estimation of the
non-inferior solution set of the problem, a procedure based on a k-shortest
path algorithm was developed. This approach was applied to a well-known
sample problem and the results are discussed and compared with those
obtained using a median shortest path model.}}
@inproceedings{BruGhiImp-ESI-95,
title = {{A multi-modal approach to the location of a rapid transit line}},
author = {G. Bruno and G. Ghiani and G. Improta},
journal = {Proc. 12th EURO Summer Inst. Locational Analysis},
month = {June},
year = {1995}}
@inproceedings{BruGhiImp-IFORS-97,
title = {{Models and algorithms for the design of rapid transit networks}},
author = {G. Bruno and G. Ghiani and G. Improta},
booktitle = {Proc. 7th Int. Special Conf. IFORS, Information Systems in
Logistics and Transportation},
month = {June},
year = {1997},
abstract = {Traditional underground metro systems, rapid rail transit systems
are becoming more and more common to improve mobility in large urban
areas. The design of such systems is a very critical task which has long
term effects on modal aplit. Decisions are to be made about topological
configuration, the number and location of lines and stations, line frequencies
etc.. In this context decision making is a complex job as several players
are involved, some objectives are unquantifiable and estimation of the
non-inferior solutions set considering the two main quantifiable objectives
(e.g. the construction cost and a measure of the social benefit); second,
the choice, among the previously selected solutions, of the most suitable
configuration by means of the remaining objectives. In the present paper
we tackle the first step generalising a k-shortest path technique in
such a way to consider complex topological patterns (grids, stars, cartwheels,
triangles etc.). The proposed method was used to simulate the Rome metro
system.}}
@article{BruHam-EJOR-89,
title = {{$K$-optimal solution sets for some polynomially solvable scheduling
problems}},
author = {Peter Brucker and Horst W. Hamacher},
journal = {Eur. J. Operational Research},
volume = {41},
number = {2},
pages = {194--202},
year = {1989},
review = {MR-90e-90069}}
@article{MR-90e-90069,
reviews = {BruHam-EJOR-89},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{$K$-optimal solution sets for some polynomially solvable scheduling
problems}},
volume = {90e},
number = {90069},
year = {1990},
text = {A $k$-optimal solution set $\Omega=\{S\sb 1,\cdots,S\sb k\}$ of
a given scheduling problem is a set of schedules such that no schedule
$S$ which is not contained in $\Omega$ is better than any $S\sb i$, $i=1,
\cdots,k$. $k$-optimal sets are useful in offering alternatives to a
single optimal schedule. In this paper algorithms are presented which
compute $k$-optimal sets for various scheduling problems for which the
optimal schedule can be computed in polynomial time.}}
@inproceedings{BurHaf-SEC-74,
title = {{A ranking problem on graphs}},
author = {R. N. Burns and Charles Edward Haff},
booktitle = {Proc. 5th Southeast Conf. Combinatorics, Graph Theory {\&} Computing},
number = {11},
series = {Graph Theory and Computing},
publisher = {Utilitas Mathematica Publishing},
address = {Winnepeg, Canada},
pages = {461--470},
year = {1974}}
@inproceedings{BusLocOls-GC-94,
title = {{Dynamic $K$-shortest path (DKSP) facility restoration algorithm}},
author = {M. T. Busche and C. M. Lockhart and C. Olszewski},
booktitle = {GLOBECOM, Communications: The Global Bridge},
publisher = {IEEE},
volume = {1},
pages = {536--542},
year = {1994},
abstract = {This paper describes the dynamic $K$-shortest path (DKSP) algorithm
for distributed facility restoration and its performance in a simulation
of AT{\&}T's high-capacity digital facilities network. The guiding paradigm
of this algorithm is that of a switched network. At each facility node
in the network, a local controller (LC) directs the activities of a digital
cross-connect system (DCS) to route high-capacity digital connections
around failures. The LCs communicate with each other via a connectionless
network using routers and signaling links embedded in the transmission
systems between nodes. After a failure, the LCs disseminate information
about failed transmission links to the whole network. High-capacity digital
connections are then restored by a call-control protocol. The simulation
shows that the algorithm's efficiency is close to that of a centralized
algorithm, and that its rate of finding alternate routes in this large
network is approximately 50 ms per restoration path.}}
@phdthesis{Bye-PhD-82,
title = {{Optimal and Near-Optimal Policies for Discrete Deterministic
Dynamic Programming Models}},
author = {Thomas Hancock Byers},
school = {Univ. of California, Berkeley, Dept. of Economics},
year = {1982},
abstract = {A new algorithm for finding policies with objective function
values in a neighborhood of the optimum for certain dynamic programming
models is presented and compared to the best available algorithms. The
algorithm combines the 'depth-first' search with 'stacking' techniques
of theoretical computer science and principles from dynamic programming
to modify the usual backtracking routine and list all near-optimal policies.
This is the first practical algorithm for a variety of large problems
that are of interest. Two such problems are critical path analysis in
project management and sequence alignment in molecular biology.}}
@article{ByeWat-OR-84,
title = {{Determining all optimal and near-optimal solutions when solving
shortest path problems by dynamic programming}},
author = {Thomas Hancock Byers and Michael S. Waterman},
journal = {Operations Research},
volume = {32},
pages = {1381--1384},
year = {1984},
abstract = {Presents a new algorithm for finding all solutions with objective
function values in the neighborhood of the optimum for certain dynamic
programming models, including shortest path problems. The new algorithm
combines the depth-first search with stacking techniques of theoretical
computer science and principles from dynamic programming to modify the
usual backtracking routine and lists all near-optimal policies. The resulting
procedure is the first practical algorithm for a variety of large problems
that are of interest.}}
@techreport{CamFraMaf-LCE-73,
title = {{The $k$ shortest spanning trees of a graph}},
author = {P. M. Camerini and L. Fratta and F. Maffioli},
institution = {IEEE-LCE Politechnico di Milano, Italy},
number = {73-10},
year = {1973}}
@article{CamFraMaf-Nw-80,
title = {{The $k$ best spanning arborescences of a network}},
author = {P. M. Camerini and L. Fratta and F. Maffioli},
journal = {Networks},
volume = {10},
number = {2},
pages = {91--110},
year = {1980},
review = {MR-81h-68023}}
@article{MR-81h-68023,
reviews = {CamFraMaf-Nw-80},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{The $k$ best spanning arborescences of a network}},
author = {Lawrence V. Saxton},
volume = {81h},
number = {68023},
year = {1981},
text = {The authors exhibit an efficient algorithm (in terms of both time
and space) for finding the $K$ best spanning arborescences (i.e. a branching
with a unique root) of a network. The algorithm given for the best arborescence
is an adaptation of Tarjan's algorithm for finding the optimum branching
of a network. To this is added a procedure for finding the next best
spanning arborescence. The result is an algorithm for finding the $K$
best spanning arborescences of a network of $n$ vertices and $m$ edges
in time $O(Km\log n)$ and space $O(K+m)$. They also note that, for dense
networks, the algorithm can be modified to operate in time $O(n^2)$.}}
@article{CarLiLut-DAM-97,
title = {{Reliability evaluation of large telecommunication networks}},
author = {Jacques Carlier and Yu Li and Jean-Luc Lutton},
journal = {Discrete Applied Mathematics},
volume = {76},
pages = {61--80},
month = {June},
year = {1997},
abstract = {In this paper, we describe an approximation method to evaluate
the reliability of large telecommunication networks based on optic fibre
and digital cross-connect systems (DCS). The reliability measures are
defined as the availability and the expected lost traffic. Their evaluation
is decomposed into the rerouting calculation and the probabilistic calculation.
The rerouting calculation (restoration from failures) is accomplished
by a heuristic method using the $K$-shortest paths. It is made very
rapidly, thanks to a sophisticated data structure. The probabilistic
calculation is based on the stratified sampling which results in computational
savings of several orders of magnitude and is well suited to very large
networks with high reliability components.},
review = {MR-98c-90035}}
@article{MR-98c-90035,
reviews = {CarLiLut-DAM-97},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Reliability evaluation of large telecommunication networks}},
volume = {98c},
number = {90035},
year = {1998}}
@inproceedings{CarSod-SOR-83,
title = {{A binary enumeration tree to find $K$ shortest paths}},
author = {Paulo Carraresi and Claudio Sodini},
booktitle = {Proc. 7th Symp. Operations Research},
number = {45},
series = {Methods of Operations Research},
publisher = {Athen{\"a}um/Hain/Hanstein},
pages = {177--188},
year = {1983},
review = {MR-85i-90053}}
@article{MR-85i-90053,
reviews = {CarSod-SOR-83},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A binary enumeration tree to find $K$ shortest paths}},
volume = {85i},
number = {90053},
year = {1985},
text = {The $K$ shortest simple paths problem in a directed graph is considered.
A procedure based on a binary enumeration tree yields the solution by
computing $K-1$ `second shortest paths' in appropriate graphs. The latter
problems are shown to be related to the determination of the best basis
adjacent to the optimal one in a minimum cost network flow problem, for
which a dual approach is proposed.}}
@inproceedings{CasRusVit-STS-97,
title = {{Stochastic user equilibrium assignment with explicit path enumeration:
comparison of models and algorithms}},
author = {E. Cascetta and Francesco Russo and Antonino Vitetta},
booktitle = {Proc. 8th Int. Symp. Transportation Systems},
year = {1997},
abstract = {In this paper a preliminary analysis of alternative models
for ``feasible'' path generation and choice is presented. In particular
a k-shortest path multi-criteria model for path enumeration is explored
and different choice models (Logit, recently proposed C-Logit and Probit)
are tested by comparing SUE assignment link flows with counts on an urban
road network. Flows are also compared for more traditional DUE and SUE
Probit implicit path enumeration models. The results obtained show that
a limited number (4-7) of paths generated with rather ``simple'' criteria
give satisfactory results, SUE with explicit path enumeration is largely
comparible with, and in some cases superior to, traditional implicit
SUE and DUE models. Explicit path enumeration allow also the specification
of more sophisticated non additive attributes in the utility function
of route choice models. From the computational point of view the explicit
path C-Logit and Probit SUE algorithms are from three to twenty times
superior to the implicit Probit SUE assignment.}}
@inproceedings{Cha-CPM-94,
title = {{Computing all suboptimal alignments in linear space}},
author = {Kun-Mao Chao},
booktitle = {Proc. 5th Symp. Combinatorial Pattern Matching},
number = {807},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {31--42},
year = {1994}}
@article{Cha-CT-68,
title = {{Generation of trees, two-trees, and storage of master forests}},
author = {J. P. Char},
journal = {Trans. Circuit Theory},
publisher = {IEEE},
volume = {CT-15},
pages = {228--238},
year = {1968},
review = {MR-39-6779}}
@article{MR-39-6779,
reviews = {Cha-CT-68},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Generation of trees, two-trees, and storage of master forests}},
volume = {39},
number = {6779},
year = {1970}}
@article{Cha-IS-98,
title = {{On computing all suboptimal alignments}},
author = {Kun-Mao Chao},
journal = {Information Sciences},
volume = {105},
number = {1--4},
pages = {189--207},
month = {March},
year = {1998},
abstract = {Naor and Brutlag [D. Naor, D. Brutlag, Proceedings of the Fourth
Symposium on Combinational Pattern Matching, Lecture Notes in Computer
Science, 684 (1993) 179-196] proposed a new compact representation for
suboptimal alignments. The kernel of that representation is a minimal
directed acyclic graph (DAG) containing all suboptimal alignments. In
this paper, a flexible space-saving scheme for computing such a DAG is
proposed. In spite of the need for storing the DAG, these methods require
very little additional working space. For two sequences of lengths M
and N (M less than or equal to N), the general scheme runs in O(MN log(1/Upsilon))
time and O(M-Upsilon(M + N)) space for arbitrarily small 0 {$<$} Upsilon
{$<$} 1. As a consequence, the worst-case running time is O(MN log log M)
using only O(N) space. A variant of the method restricts the log log
M factor to affect only grid points lying between suboptimal alignments.
It is also shown that a running time of O(MN) can be achieved by using
only O(M1+epsilon + N) space for arbitrarily small constant epsilon {$>$}
0. To exploit the computed DAG, a variant of Aho-Corasick pattern matching
machine [A.V. Aho, M.J. Corasick,
Comm. ACM 18 (1975) 333-340] is employed to locate all occurrences of
specified patterns, and then a path is found in the DAG that maximizes
the sum of the scores of the non-overlapping patterns occurring in it.
An example illustrates the utility.}}
@phdthesis{Cha-PhD-84,
title = {{Design and Analysis of Graph Algorithms: Spanning Tree Enumeration,
Planar Embedding and Maximal Planarization}},
author = {Rajagopalan Jayakumar},
school = {Concordia Univ., Dept. Electronics and Electrical Engineering},
year = {1984},
abstract = {In Part I of this thesis, a detailed computational complexity
analysis of a spanning tree enumeration algorithm due to Char is given.
An expression for the number of sequences generated by the algorithm
when applied on a general graph is derived. The complexity of this algorithm
is shown to be $O(n^3 t)$ where $n$ is the number of vertices of the
graph and $t$ is the number of spanning trees. Two heuristics aimed at
reducing the number of sequences generated are proposed for selecting
the initial spanning tree and an implementation using path compression
is described. A class of special graphs for which the algorithm is of
complexity $O(nt)$ is identified. Certain interesting results relating
to the complete graph, the ladder, and the wheel, which belong to this
class, are obtained. An efficient implementation of Char's algorithm,
called algorithm MOD-CHAR, is developed. Classes of graphs for which
algorithm MOD-CHAR is of complexity $O(nt)$ are identified. It is shown
that for large complete graphs ($n\ge 8$), algorithm MOD-CHAR requires,
on the average, at most 10 computational steps to generate a spanning
tree. A computational evaluation of Char's algorithm in comparison with
Gabow and Myers' algorithm is presented. In Part II, efficient algorithms
to obtain a planar embedding of a planar graph and to determine a maximal
planar subgraph of a nonplanar graph are developed. An embedding procedure
which involves placing the vertices at different horizontal and vertical
levels in the plane is developed. The vertical levels of the vertices
are decided by their st-numbers and an $O(n)$ algorithm is presented
to determine the horizontal levels of the vertices. Another $O(n)$ algorithm
to determine the order in which edges entering a vertex from lower numbered
vertices should be drawn is developed. A procedure to draw by hand the
edges without crossovers is described. It is shown that a planarization
algorithm due to Ozawa and Takahashi does not, in general, determine
a maximal planar subgraph. A new maximal planarization algorithm of complexity
$O(n^2)$ is developed.}}
@article{ChaMil-Algo-95,
title = {{Linear-space algorithms that build local alignments from fragments}},
author = {Kun-Mao Chao and Webb Miller},
journal = {Algorithmica},
volume = {13},
pages = {106--134},
year = {1995},
review = {MR-95j-92011}}
@article{MR-95j-92011,
reviews = {ChaMil-Algo-95},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Linear-space algorithms that build local alignments from fragments}},
author = {Dietmar Dorninger},
volume = {95j},
number = {92011},
year = {1995},
text = {Given two sequences $A=a\sb 1,a\sb 2,\cdots,a\sb M$ and $B=b\sb
1,b\sb 2,\cdots,b\sb N$, a fragment $f=(i,j,k)$ is defined by $a\sb i=b\sb
j$, $a\sb {i+1}=b\sb {j+1},\cdots,a\sb {i+k-1}=b\sb {j+k-1}$ and the
property that $f$ is not properly contained in another fragment. The
set $F$ of all fragments in respect to $A$ and $B$ can be partially ordered
by the relation $(i,j,k)<(i',j',k')$ iff $i'+k'\leq i$ and $j'+k'\leq
j$. An alignment is a sequence $f\sb 1,f\sb 2,\cdots,f\sb r$ in $F$ with
$f\sb i>f\sb {i+1}$ for $i=1,2,\cdots,r-1$. By assigning scores to fragments
and gaps, the question arises as to how to find an alignment for which
the sum of fragment scores minus penalties for gaps is highest. By assuming
affine gap functions and combining a time efficient dynamic programming
method with a space saving approach, the authors develop an alignment
algorithm that uses $O((M+N+\vert F\vert \log N)\log M)$ time and $O(M+N)$
storage.
By removing all fragments of a highest scoring alignment from $F$ and
determining a highest scoring alignment from the fragments remaining
in $F$, and by further repeating this procedure, one obtains the $n$
best nonintersecting alignments. A time efficient algorithm using linear
space to compute the $n$ best nonintersecting alignments for preassigned
$n$ is constructed and the utility of it is demonstrated by an example
from DNA-comparison.}}
@article{Che-COR-93,
title = {{An algorithm for finding the $k$ quickest paths in a network}},
author = {Yen-Liang Chen},
journal = {Computers and Operations Research},
volume = {20},
pages = {59--65},
year = {1993},
abstract = {Let $N$ be a network with n nodes and m arcs, and let $\sigma$
be the amount of data to be transmitted. The quickest path problem is
to find a routing path in $N$ such that the time required to ship $\sigma$
units of data from the source to the sink is minimum. The problem considered
is to find the first $k$ quickest looping paths from the source to the
sink, and an algorithm with time complexity of $O(m^2+(m+k)n\log{n}+k^{3/2}\log{k})$
is developed.}}
@article{Che-IPL-94,
title = {{Finding the $k$ quickest simple paths in a network}},
author = {Yen-Liang Chen},
journal = {Information Processing Letters},
volume = {50},
pages = {89--92},
year = {1994}}
@article{CheHam-DAM-87,
title = {{Algorithms for finding $K$-best perfect matchings}},
author = {Chandra R. Chegireddy and Horst W. Hamacher},
journal = {Discrete Applied Mathematics},
volume = {18},
pages = {155--165},
year = {1987},
review = {MR-89j-90209}}
@article{MR-89j-90209,
reviews = {CheHam-DAM-87},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Algorithms for finding $K$-best perfect matchings}},
volume = {89j},
number = {90209},
year = {1989},
text = {In the $K$-best perfect matching problem $(K{\rm M})$ one wants
to find $K$ pairwise different, perfect matchings $M\sb 1,\cdots,M\sb
K$ such that $w(M\sb 1)\ge w(M\sb 2)\ge\cdots\ge w(M\sb K)\ge w(M)$,
for all $M\not= M\sb 1,M\sb 2,\cdots,M\sb K$. The procedure discussed
in this paper is based on a binary partitioning of the matching solution
space. We survey different algorithms to perform this partitioning. The
best complexity bound of the resulting algorithms discussed is $O(Kn\sp
3)$, where $n$ is the number of nodes in the graph.}}
@article{CheHun-COR-94,
title = {{Algorithms for the constrained quickest path problem and the
enumeration of quickest paths}},
author = {G.-H. Chen and Y.-C. Hung},
journal = {Computers and Operations Research},
volume = {21},
pages = {113--118},
year = {1994},
abstract = {The quickest path problem, originally proposed by Chen and
Chin (1989), is a variant of the shortest path problem. Its objective
is to find quickest paths in a network to transmit a given amount of
data such that the transmission time is minimized. If the quickest paths
are required to go through a specified path, then the restricted problem
is called the constrained quickest path problem. In this paper, for all
pairs of nodes in a network $N$, an $O(mn^2)$ time algorithm is first
presented to find constrained quickest paths, and then an $O(k^2mn^2)$
time algorithm is presented to enumerate the first $k$ quickest paths.
The results improve previous results by Rosen, Sun and Xue (1991).}}
@techreport{CheRinTan-WP-97,
title = {{The first $K$ minimum time paths in a time-schedule network}},
author = {Yen-Liang Chen and Dan Rinks and Kwei Tang},
type = {Working Paper},
institution = {Louisiana State Univ., Dept. of Information Systems and
Decision Sciences},
number = {9708},
year = {1997},
url = {http://www.bus.lsu.edu/isds/chun/wpapers/9708.htm},
abstract = {The time-constrained shortest path problem is an important
generalization of the shortest path problem and has attracted much research
interest in recent years. In this paper, we consider a time constraint
commonly encountered in practice; namely, time-schedule constraint, which
assumes that every node in the network has a list of pre-specified departure
times and requires that departure from a node take place only at one
of the departure times. Two problems associated with the first K minimum
time paths in a time-schedule network are considered. The first is to
find the first K loopless minimum time paths, in which all the nodes
in a path are distinct, and the second is to find the first K minimum
time looping paths, in which a path may pass through some nodes more
than one time. For both problems, efficient polynomial time algorithms
are developed.}}
@inproceedings{CheSoo-ASSP-94,
title = {{An $N$-best candidates-based discriminative training for speech
recognition applications}},
author = {Jung-Kuei Chen and F. K. Soong},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {I/625--628},
month = {April},
year = {1994}}
@article{CheSoo-TSAP-94,
title = {{An $N$-best candidates-based discriminative training for speech
recognition applications}},
author = {Jung-Kuei Chen and F. K. Soong},
journal = {Trans. Speech {\&} Audio Processing},
publisher = {IEEE},
volume = {2},
number = {1, part 2},
pages = {206--216},
month = {January},
year = {1994},
abstract = {The authors propose an $N$-best candidates-based discriminative
training procedure for constructing high-performance HMM speech recognizers.
The algorithm has two distinct features: $N$-best hypotheses are used
for training discriminative models; and a new frame-level loss function
is minimized to improve the separation between the correct and incorrect
hypotheses. The $N$-best candidates are decoded based on their recently
proposed tree-trellis fast search algorithm. The new frame-level loss
function, which is defined as a halfwave rectified log-likelihood difference
between the correct and competing hypotheses, is minimized over all training
tokens. The minimization is carried out by adjusting the HMM parameters
along a gradient descent direction. Two speech recognition applications
have been tested, including a speaker independent, small vocabulary (ten
Mandarin Chinese digits), continuous speech recognition, and a speaker-trained,
large vocabulary (5000 commonly used Chinese words), isolated word recognition.
Significant performance improvement over the traditional maximum likelihood
trained HMMs has been obtained. In the connected Chinese digit recognition
experiment, the string error rate is reduced from 17.0 to 10.8{\%} for unknown
length decoding and from 8.2 to 5.2{\%} for known length decoding. In the
large vocabulary, isolated word recognition experiment, the recognition
error rate is reduced from 7.2 to 3.8{\%}. Additionally, they have found
that using more relaxed decoding constraints in preparing $N$-best hypotheses
yields better recognition results.}}
@inproceedings{CheSooLee-ASSP-94,
title = {{Large vocabulary word recognition based on tree-trellis search}},
author = {Jung-Kuei Chen and F. K. Soong and Lin-Shan Lee},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {2},
pages = {II/137--140},
month = {April},
year = {1994},
abstract = {In this paper we propose a large vocabulary (90000 words),
Chinese (Mandarin) word recognizer based on the tree-trellis fast search
algorithm. The recognizer is divided into 3 modules: local likelihood
computation, a forward trellis search and a backward tree search. In
the forward trellis search, a free syllable decoding is performed without
a language model and a partial path map is created. The best-first tree
search is then applied backward along a lexicon, which is arranged as
a syllabic tree, to find the $N$-best word candidates. In the experiment,
context-dependent subsyllabic HMMs were trained with a new discriminative
training method. When it is evaluated on a speaker-trained database,
the recognizer achieved a word error rate of 5{\%} for the full size (90000
words) vocabulary and 1.7{\%} for a smaller subset (5000 words) vocabulary.
A real-time demo system has also been implemented on an SGI R-4000 workstation.}}
@article{ChiChe-CSSE-97,
title = {{Block-switch networks: a cost-effective class of interconnection
networks}},
author = {Wei-Kuo Chiang and Rong-Jaye Chen},
journal = {Computer Systems Science and Engineering},
volume = {12},
number = {3},
pages = {175--185},
month = {May},
year = {1997},
abstract = {A new interconnection scheme is proposed for hierarchically
constructing massively parallel systems, called the block-switch network
(BSN). The authors present a method of connecting together a number of
identical basic atoms level by level, a basic atom being an arbitrary
connected graph. A BSN is characterized by (G,m), where G represents
the basic atom and m denotes the number of levels in hierarchical expansion.
A particular choice for G yields a family of hierarchical networks. The
topological properties of the BSN for the general case are investigated,
and then the results gained from applying BSN to different basic atoms
are also discussed. The BSN enables us to construct new families of graphs
more feasible and cost-effective. A shortest-path routing algorithm for
the BSN is derived by reducing the routing problem to the K-best perfect
matching problem. In particular the authors implement fundamental parallel
algorithms (descend/ascend) on the BSN(Q/sub n/,m) where Q/sub n/ denotes
an n-cube, and demonstrate that the performance on the BSN(Q/sub n/,m)
is very close to that of the comparable hypercube.}}
@article{ChoBur-TPAS-84,
title = {{Transmission line route selection: An application of $K$-shortest
paths and goal programming}},
author = {F. Choobineh and T. Burgman},
journal = {Trans. Power Apparatus and Systems},
publisher = {IEEE},
volume = {PAS-103},
pages = {3253--3259},
year = {1984},
abstract = {A two-stage solution procedure is developed as a managerial
decision-making tool in the transmission line route selection process.
In stage one, the K least costly alternatives are found, based strictly
on monetary considerations. In stage two, the alternative which causes
the least amount of social and environmental disruption is selected from
the alternatives generated in stage one.}}
@article{ChoLeeJua-PRAI-94,
title = {{A minimum error rate pattern recognition approach to speech recognition}},
author = {W. Chou and C.-H. Lee and B.-H. Juang and F. K. Soong},
journal = {Int. J. Pattern Recognition {\&} Artificial Intelligence},
volume = {8},
number = {1},
pages = {5--31},
month = {February},
year = {1994},
abstract = {In this paper, a minimum error rate pattern recognition approach
to speech recognition is studied with particular emphasis on the speech
recognizer designs based on hidden Markov models (HMMs) and Viterbi decoding.
This approach differs from the traditional maximum likelihood based approach
in that the objective of the recognition error rate minimization is established
through a specially designed loss function, and is not based on the assumptions
made about the speech generation process. Various theoretical and practical
issues concerning this minimum error rate pattern recognition approach
in speech recognition are investigated. The formulation and the algorithmic
structures of several minimum error rate training algorithms for an HMM-based
speech recognizer are discussed. The tree-trellis based $N$-best decoding
method and a robust speech recognition scheme based on the combined string
models are described. This approach can be applied to large vocabulary,
continuous speech recognition tasks and to speech recognizers using word
or subword based speech recognition units. Various experimental results
have shown that significant error rate reduction can be achieved through
the proposed approach.}}
@inproceedings{ChoMadMor-ICCI-95,
title = {{On finding single-source single-destination $k$ shortest paths}},
author = {Eugene Inseok Chong and Sanjeev Rao Maddila and Steven Todd Morley},
booktitle = {Proc. 7th Int. Conf. Computing and Information},
month = {July},
year = {1995},
url = {http://phoenix.trentu.ca/jci/papers/icci95/A206/P001.html},
abstract = {The shortest path algorithms have a wide range of applications
and much research has been devoted to the subject. While finding a shortest
path in a digraph is relatively easy, finding $k$ shortest paths is not
an easy task, especially for a single-source and single-destination pair.
In this paper, we present an algorithm for finding $k$ shortest paths
for a source-destination pair. Our algorithm is applicable to any digraphs
without negative weights. The paths are not necessarily simple, but if
the digraphs are acyclic, the paths found will be simple. Given a digraph
of $n$ vertices and $m$ edges, our algorithm runs in time $O(km\log(kn)+k^2m)$
and space $O(kn)$. Our algorithm is an extension of Dijkstra's algorithm,
easy to implement, and generates the $k$ shortest paths in the order
of the path length.}}
@inproceedings{ChoMatJua-ASSP-94,
title = {{An algorithm of high resolution and efficient multiple string
hypothesization for continuous speech recognition using inter-word models}},
author = {W. Chou and T. Matsuoka and B.-H. Juang and C.-H. Lee},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {2},
pages = {II/153--156},
month = {April},
year = {1994},
abstract = {We propose a new accurate string hypothesization algorithm
to find the $N$-best multiple string hypotheses in continuous speech
recognition. The algorithm differs from the conventional $N$-best search
algorithms in that it allows the use of the same set of long term language
model scores and the detailed context-dependent subword models such as
inter-word context dependent triphone models in both forward and backward
search for high performance speech recognition. It is an extension of
the tree-trellis $N$-best search algorithm(1). The inter-word context
dependency is exactly preserved in both forward partial path map preparation
and the proposed backward $N$-best multiple string hypothesis tree search.
The search efficiency is maximized by applying the same high resolution
acoustic and language models in both search directions. When search heuristics
are used, the proposed approach provides a more accurate string model
matching than that of the conventional frame-synchronous Viterbi beam
search decoder.}}
@inproceedings{ChoSch-SNLW-89,
title = {{The $N$-best algorithm: an efficient search procedure for finding
top $N$ sentence hypotheses}},
author = {Yen-Lu Chow and Richard Schwartz},
booktitle = {Proc. DARPA Speech {\&} Natural Language Worksh.},
pages = {199--202},
year = {1989}}
@inproceedings{Chu-RECOMB-97,
title = {{Monte Carlo sequence alignment}},
author = {Gary A. Churchill},
booktitle = {Proc. 1st Int. Conf. Computational Molecular Biology},
publisher = {ACM},
pages = {93--97},
month = {January},
year = {1997},
summary = {Extracted from various points in this paper (which lacks an
abstract): ``The alignment of molecular sequences is a problem central
to many important questions in molecular biology. ... The problem studied
here lies at the intersection of two lines of research. The first is
concerned with the sensitivity of alignments to choice of scores. ...
A second line of research is the study of suboptimal alignments. This
work has been driven by the observation that an optimal alignment is
not necessarily a biologically correct alignment. However, biologically
correct alignments are often nearly optimal when the scoring system is
well chosen. A recent review of suboptimal alignment methods is provided
by Vingron [Vin-COSB-96]. ... Our goal in this work is to develop algorithms
to sample from the marginal posterior distribution of an alignment. ...
Pairwise alignments can be represented as a directed graph on a two dimensional
grid ... An alignment is shown as a path, a connected sequence of arcs,
traversing the matrix from the upper left vertex to the lower right vertex
by a series of east, southeast, and south moves. ... The algorithm employed
to sample from the distribution is similar in style to standard dynamic
programming. A forward pass through the matrix is used to compute conditional
probabilities for partial alignments that end with each node in the path
graph. However, instead of choosing the optimal score at each step, our
algorithm sums over the three arcs entering the node.''}}
@article{ClaKriRau-SIAM-63,
title = {{Computing the $N$ best loopless paths in a network}},
author = {S. Clarke and A. Krikorian and J. Rausen},
journal = {J. SIAM},
publisher = {SIAM},
volume = {11},
pages = {1096--1102},
year = {1963}}
@article{ColDayNel-Algs-89,
title = {{Unranking and ranking spanning trees of a graph}},
author = {Charles Joseph Colbourn and R. P. J. Day and L. D. Nel},
journal = {J. Algorithms},
volume = {10},
number = {2},
pages = {271--286},
month = {June},
year = {1989},
abstract = {The set $S$ of spanning trees of an $n$-vertex graph $G$ can
be placed in one-to-one correspondence with the interval $(1,s)$ where
$s=|S|$. The authors develop $O(n^3)$ unranking and ranking functions
for the spanning trees of an arbitrary graph. The unranking function
maps any interval $(1,s)$ to the corresponding tree, while the ranking
function maps a spanning tree to the appropriate index in the interval.
The unranking function provides an $O(n^3)$ method for generating a random
spanning tree of a graph with uniform distribution.},
review = {MR-90g-68060}}
@article{MR-90g-68060,
reviews = {ColDayNel-Algs-89},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Unranking and ranking spanning trees of a graph}},
volume = {90g},
number = {68060},
year = {1990}}
@article{ColMyrNeu-Algs-96,
title = {{Two algorithms for unranking arborescences}},
author = {Charles Joseph Colbourn and Wendy J. Myrvold and Eugene Neufeld},
journal = {J. Algorithms},
volume = {20},
number = {2},
pages = {268--281},
year = {1996},
abstract = {Colbourn, Day, and Nel developed the first algorithm requiring
at most $O(n^3)$ arithmetic operations for ranking and unranking spanning
trees of a graph ($n$ is the number of vertices of the graph). We present
two algorithms for the more general problem of ranking and unranking
rooted spanning arborescences of a directed graph. The first is conceptually
very simple and requires $O(n^3)$ arithmetic operations. The second approach
shows that the number of arithmetic operations can be reduced to the
same as that of the best known algorithms for matrix multiplication.},
review = {MR-97d-68154}}
@article{MR-97d-68154,
reviews = {ColMyrNeu-Algs-96},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Two algorithms for unranking arborescences}},
volume = {97d},
number = {68154},
year = {1997}}
@inproceedings{ConPec-AIRO-95,
title = {{Using simulated annealing to solve the $K$-shortest path problem}},
author = {Andrea Consiglio and Antonio Pecorella},
booktitle = {Proc. AIRO 1995},
publisher = {Associazione Italiana Ricerca Operativa},
month = {September},
year = {1995}}
@article{CouCliCur-COR-99,
title = {{An interactive bi-objective shortest path approach: searching
for unsupported nondominated solutions}},
author = {J. M. Coutinho-Rodrigues and J. C. N. Cl{\'\i}maco and John Richard
Current},
journal = {Computers and Operations Research},
volume = {26},
number = {8},
pages = {789--798},
month = {July},
year = {1999},
abstract = {In many network routing problems, several conflicting objectives
must be considered. Even for the bi-objective shortest path problem,
generating and presenting the whole set of nondominated solutions (paths)
to a decision maker, in general, is not effective because the number
of these paths can be very large. Interactive procedures are adequate
to overcome these drawbacks. J.R. Current et al. (1990) proposed an interactive
approach based on a NISE-like procedure (J. Cohon, 1978) to search for
nondominated supported solutions and using auxiliar constrained shortest
path problems to carry out the search inside the duality gaps. We propose
a new interactive approach to search for unsupported nondominated solutions
(lying inside duality gaps) based on a k-shortest path procedure. Both
approaches are compared.}}
@inproceedings{CoxHin-ICPR-94,
title = {{An efficient implementation of Reid's multiple hypothesis tracking
algorithm and its evaluation for the purpose of visual tracking}},
author = {Ingemar J. Cox and S. L. Hingorani},
booktitle = {Proc. 12th Int. Conf. Pattern Recognition},
publisher = {IEEE},
volume = {1},
pages = {437--442},
year = {1994},
abstract = {An efficient implementation of Reid's multiple hypothesis tracking
(MHT) algorithm is presented in which the the k-best hypotheses are determined
in polynomial time using an algorithm due to Murty (1968). The MHT algorithm
is then applied to several motion sequences. The MHT capabilities of
track initiation, termination and continuation are demonstrated. Continuation
allows the MHT to function despite temporary occlusion of tracks. Between
50 and 150 corner features are simultaneously tracked in the image plane
over a sequence of up to 60 frames. Each corner is tracked using a simple
linear Kalman filter and any data association uncertainty is resolved
by the MHT. Kalman filter parameter estimation is discussed and experimental
results show that the algorithm is robust to errors in the motion model.}}
@article{CoxHin-PAMI-96,
title = {{An efficient implementation of Reid's multiple hypothesis tracking
algorithm and its evaluation for the purpose of visual tracking}},
author = {Ingemar J. Cox and S. L. Hingorani},
journal = {Trans. Pattern Analysis and Machine Intelligence},
publisher = {IEEE},
volume = {18},
pages = {138--150},
year = {1996},
abstract = {An efficient implementation of Reid's multiple hypothesis tracking
(MHT) algorithm is presented in which the k-best hypotheses are determined
in polynomial time using an algorithm due to Murly (1968). The MHT algorithm
is then applied to several motion sequences. The MHT capabilities of
track initiation, termination, and continuation are demonstrated together
with the latter's capability to provide low level support of temporary
occlusion of tracks. Between 50 and 150 corner features are simultaneously
tracked in the image plane over a sequence of up to 51 frames. Each corner
is tracked using a simple linear Kalman filter and any data association
uncertainty is resolved by the MHT. Kalman filter parameter estimation
is discussed, and experimental results show that the algorithm is robust
to errors in the motion model. An investigation of the performance of
the algorithm as a function of look-ahead (tree depth) indicates that
high accuracy can be obtained for tree depths as shallow as three. Experimental
results suggest that a real-time MHT solution to the motion correspondence
problem is possible for certain classes of scenes.}}
@article{CoxMil-TAES-95,
title = {{On finding ranked assignments with application to multitarget
tracking and motion correspondence}},
author = {Ingemar J. Cox and Matt L. Miller},
journal = {Trans. Aerospace and Electronic Systems},
publisher = {IEEE},
volume = {31},
pages = {486--489},
year = {1995},
abstract = {Within the target tracking community there is strong interest
in computing a ranked set of assignments of measurements to targets.
These k-best assignments are then used to determine good approximations
to the data association problem. Much earlier work described algorithms
which either had exponential worst case time or were not guaranteed to
return the k-best assignments. Danchick and Newnam (1993) described a
fast algorithm for finding the exact k-best hypotheses. However, in the
worst case, k! linear assignment problems must be solved. This correspondence
describes an algorithm originally due to Murty (1968) for optimally determining
a ranked set of assignments in polynomial time and which is linear in
k.}}
@article{CoxMilDan-TAES-97,
title = {{A comparison of two algorithms for determining ranked assignments
with application to multitarget tracking and motion correspondence}},
author = {Ingemar J. Cox and Matt L. Miller and R. Danchick and G. E. Newnam},
journal = {Trans. Aerospace and Electronic Systems},
publisher = {IEEE},
volume = {33},
number = {1},
pages = {295--301},
month = {January},
year = {1997},
abstract = {Recently, it has become clear that determining a ranked set
of assignments allows computation of very good approximations to the
data association problem. Several algorithms have been proposed but only
two return the k-best assignments in reasonable time. One is Danchick
and Newnams' [1993] algorithm, which is based on the recognition that
determining the best assignment is a classical assignment problem and
that determining a ranked set of assignments may be accomplished by solving
a series of modified copies of the initial assignment problem. The other
algorithm is originally due to Murty [1968] and was most recently described
within the context of multitarget tracking. We evaluate the two algorithm
using randomly generated data and data obtained from an electrooptical
sensor simulation in which 90 missiles are launched. These evaluations
show that Murty's algorithm perform significantly better in all scenarios.
We show the relationship between the two algorithms and how Danchick
and Newnam's algorithm can be very easily modified to Murty's algorithm.
Experimental results using Murty's algorithm suggest that a solution
to the real-time data association problem is now feasible.}}
@article{CurReVCoh-TS-87,
title = {{The median shortest path problem: a multiobjective approach to
analyze cost vs. accessibility in the design of transportation networks}},
author = {John Richard Current and Charles S. ReVelle and Jared Leigh Cohon},
journal = {Transportation Science},
volume = {21},
number = {3},
pages = {188--197},
year = {1987},
review = {MR-88h-90067}}
@article{MR-88h-90067,
reviews = {CurReVCoh-TS-87},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{The median shortest path problem: a multiobjective approach to
analyze cost vs. accessibility in the design of transportation networks}},
volume = {88h},
number = {90067},
year = {1988},
text = {We introduce the median shortest path problem (MSPP). The MSPP
is a bicriterion path problem with the objectives being the minimization
of the total path length and the minimization of the total travel time
required for demand to reach a node on the path. Potential applications
of the MSPP include, among others, the location of new highways, railroad
lines and subway lines and the design of airline routes. It is particularly
applicable in transportation network design problems where the trade-off
between operator costs and user costs is important. An algorithm is presented
to identify noninferior solutions to the MSPP. This algorithm incorporates
a $K$ shortest path algorithm. The algorithm is demonstrated with a sample
problem and the results are compared to those obtained using integer
programming.}}
@inproceedings{DaiImaIwa-ISAAC-93,
title = {{How to treat delete requests in semi-online problems}},
author = {Yang Dai and Hiroshi Imai and Kazuo Iwano and Naoki Katoh},
booktitle = {Proc. 4th Int. Symp. Algorithms and Computation},
number = {762},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {48--57},
year = {1993},
abstract = {We propose a new approach to obtain a semi-online fully dynamic
algorithm, given a partially dynamic algorithm, by introducing a new
way of handling delete requests. Briefly speaking, we are interested
in how online algorithms become more efficient with some partial knowledge
of future delete requests. A dynamic algorithm solves the problem for
the current instance every time when an add/delete request is made to
change the instance. If a dynamic algorithm allows only add requests,
we call it partially dynamic, otherwise we call it fully dynamic. An
offline algorithm gives a set of solutions of a dynamic algorithm when
the entire request sequence is known beforehand. A semi-online problem
is a special case of online problems.}}
@inproceedings{DaiLee-ICCC-94,
title = {{Parsing with tag information in a probabilistic generalized LR
parser}},
author = {Jian-Cheng Dai and Hsi-Jian Lee},
booktitle = {Proc. Int. Conf. Chinese Computing},
publisher = {Nat. Univ. Singapore},
pages = {33--39},
month = {June},
year = {1994},
abstract = {A new corpus-based probabilistic generalized LR parser is presented
for parsing Chinese sentences. Because there are generally different
tags in each word of a Chinese sentence, it is helpful to use tag information
to avoid parsing tag sequences that are unreliable with respect to a
particular input sentence. In order to use tag information conveniently,
a multi-stage input graph is constructed to represent the $N$-best tag
sequences. In the proposed parser, parse paths are formulated as a sentence
transition graph. The parser, which applies a sentence merging technique
and a hill climbing strategy, truncates unpromising partial parses quickly.
Experimental results reveal that the hill climbing strategy is more efficient
than the depth-first strategy and the proposed sentence merging technique
is also effective.}}
@article{DanNew-TAES-93,
title = {{A fast method for finding the exact $N$-best hypotheses for multitarget
tracking}},
author = {R. Danchick and G. E. Newnam},
journal = {Trans. Aerospace and Electronic Systems},
publisher = {IEEE},
volume = {29},
pages = {555--560},
year = {1993},
abstract = {The necessity for multiple hypothesis tracking (MHT) is recognized
throughout the SDI tracking community. However, implementations of MHT
techniques have required enormous amounts of computer time and memory.
An efficient method of measurement-to-target association that makes MHT
practical for the first time is presented. The method finds the exact
N-best feasible hypotheses directly from a sequence of linear assignment
problem solutions.}}
@inproceedings{Das-ICCS-85,
title = {{On search strategies for $n$ best solutions}},
author = {Das Gupta, S.},
booktitle = {Int. Conf. Cybernetics {\&} Society},
publisher = {IEEE},
pages = {664--668},
month = {November},
year = {1985},
abstract = {Search strategies of various types and forms are used to find
optimal solutions to problems in different areas to determine the 'best'
solution. In many situations it is desirable to have a collection of
n best solutions sorted on cost rather than having the unique optimal
solution. There are many heuristic search strategies in the artificial
intelligence problems where combinatorial explosion makes the search
for the optimal infeasible. In some cases it is possible to break the
problem into subproblems, obtain n-best solutions and then synthesize
the problem into an n-best solution for the whole problem. The author
proposes some search strategies for n-best solution in closed form and
using heuristics.}}
@inproceedings{DeaKelLih-GTCA-92,
title = {{The spanning tree enumeration problem for digraphs}},
author = {Nathaniel Dean and A. K. Kelmans and Keh-Wei Lih and William
A. Massey and Peter Winkler},
booktitle = {Graph Theory, Combinatorics, and Algorithms},
pages = {277--287},
year = {1992}}
@inproceedings{DenNuSam-ASSP-95,
title = {{Improved speech modeling and recognition using multi-dimensional
articulatory states as primitive speech units}},
author = {L. Deng and J. Nu and H. Sameti},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {385--388},
month = {May},
year = {1995},
abstract = {We provide a formal description of a speech recognizer designed
on the basis of elaborate articulatory timing that a asynchronous across
the multiple articulatory-feature dimensions. Three improved critical
components of the recognizer are described in detail. Evaluation results,
obtained from a standard TIMIT phonetic recognition task confined within
the $N$-best rescoring scenario, are reported on comparative performances
between the new feature-based recognizer and a recognizer using the conventional
context-dependent triphone units. The results demonstrate an overall
superior quality of the rescored $N$-best list from the feature-based
recognizer over that from the triphone-based recognizer. Greater performance
improvements are observed as the top number of candidate sentences increases.}}
@article{Der-DAM-85,
title = {{Some basic exchange properties in combinatorial optimization
and their application to constructing the $k$-best solutions}},
author = {Ulrich Derigs},
journal = {Discrete Applied Mathematics},
volume = {11},
pages = {129--141},
year = {1985},
review = {MR-86m-90124}}
@article{MR-86m-90124,
reviews = {Der-DAM-85},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Some basic exchange properties in combinatorial optimization
and their application to constructing the $k$-best solutions}},
author = {Th. M. Liebling},
volume = {86m},
number = {90124},
year = {1986},
text = {We characterize optimal, $k$-best and sets of $k$-best solutions
for a combinatorial optimization problem via simple exchange properties.
We show the relationship of this concept to the concept of adjacency
and we extend the concept to discrete optimization problems and problems
with objective functions fulfilling the cone-property. We show that those
exchange properties play a fundamental role in partitioning strategies
for finding sets of $k$-best solutions.}}
@inproceedings{Der-ICOR-84,
title = {{Exchange properties and $K$-best strategies in combinatorial
optimization}},
author = {Ulrich Derigs},
booktitle = {Proc. 10th Int. Conf. Operational Research},
publisher = {North-Holland},
pages = {393--406},
year = {1984},
abstract = {Exchange properties in set systems underlying combinatorial
optimizations problems play an important role in characterising best
and next best solutions and in partitioning strategies for ranking the
set of feasible solutions. The author exploits these basic combinatorial
principles and shows their application for some standard problems.}}
@inproceedings{DesPicKao-SSST-95,
title = {{Efficient search strategies in hierarchical pattern recognition
systems}},
author = {N. Deshmukh and J. Picone and Yu-Hung Kao},
booktitle = {Proc. 27th Southeastern Symp. System Theory},
publisher = {IEEE},
pages = {88--91},
month = {March},
year = {1995},
abstract = {We describe the generalized $N$-best search algorithm as applied
to hierarchical pattern recognition, and discuss its limitations for
a broad class of problems. We then introduce a new algorithm, called
the Frame-Synchronous Viterbi Search, that prunes hypotheses by actively
organizing system memory after each step in the search. This algorithm
is shown to save memory and computation for a specific class of problems
involving large search spaces and small memory resources. We also discuss
generalizations of this algorithm to provide true N-best scoring and
intelligent pruning while preserving the hierarchical structure of the
hypotheses. An example of a practical speech recognition system using
this algorithm is given.}}
@article{DicDrySac-IJCGA-92,
title = {{Simple algorithms for enumerating interpoint distances and finding
$k$ nearest neighbors}},
author = {Matthew T. Dickerson and R. L. Scot Drysdale and J{\"o}rg-Rudiger
Sack},
journal = {Int. J. Computational Geometry and Applications},
volume = {2},
number = {3},
pages = {221--239},
year = {1992},
review = {MR-93j-68212}}
@article{MR-93j-68212,
reviews = {DicDrySac-IJCGA-92},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Simple algorithms for enumerating interpoint distances and finding
$k$ nearest neighbors}},
volume = {93j},
number = {68212},
year = {1993},
text = {We present an $O(n\log n+k\log k)$ time and $O(n+k)$ space algorithm
which takes as input a set of $n$ points in the plane and enumerates
the $k$ smallest distances between pairs of points in nondecreasing order.
We also present an $O(n\log n+kn\log k)$ solution to the problem of finding
the $k$
nearest neighbors for each of $n$ points. Both algorithms are conceptually
very simple, are easy to implement, and are based on a common data structure:
the Delaunay triangulation. Variants of the algorithms work for any convex
distance function metric.}}
@article{DicEpp-CGTA-96,
title = {{Algorithms for proximity problems in higher dimensions}},
author = {Matthew T. Dickerson and David Eppstein},
journal = {Computational Geometry Theory and Applications},
volume = {5},
pages = {277--291},
year = {1996},
abstract = {We present algorithms for five interdistance enumeration problems
that take as input a set $S$ of $n$ points in $R^d$ (for a fixed but
arbitrary dimension $d$) and as output enumerate pairs of points in $S$
satisfying various conditions. We present: an $O(n\log{n}+k)$ time and
$O(n)$ space algorithm that takes as additional input a distance $\delta$
and outputs all $k$ pairs of points in $S$ separated by a distance of
$\delta$ or less; an $O(n\log{n}+k\log{k})$ time and $O(n+k)$ space algorithm
that enumerates in non-decreasing order the $k$ closest pairs of points
in $S$; an $O(n\log{n}+k)$ time algorithm for the same problem without
any order restrictions; an $O(nk\log{n})$ time and $O(n)$ space algorithm
that enumerates in nondecreasing order the $nk$ pairs representing the
$k$ nearest neighbors of each point in $S$; and an $O(n\log{n}+kn)$ time
algorithm for the same problem without any order restrictions. The algorithms
combine a modification of the planar approach of Dickerson, Drysdale,
and Sack with the method of Bern, Eppstein, and Gilbert for augmenting
a point set to have a linear size bounded degree Delaunay triangulation.
Thus, in addition to providing new solutions to these problems, the paper
also shows how the Delaunay triangulation can be used as the underlying
data structure in a unified approach to proximity problems even in higher
dimensions.}}
@article{DioCliNor-IEE-89,
title = {{Dynamic planning model for urban telephone networks and its applications}},
author = {J. M. B. Diogo and J. C. N. Cl{\'\i}maco and P. M. N. Nordeste and
J. M. F. Craveirinha},
booktitle = {IEE Proceedings I (Communications, Speech and Vision)},
volume = {136},
pages = {283--290},
year = {1989},
abstract = {Describes a model (ARCOS) for dynamic planning of small- and
medium-size urban telephone networks. The main innovative feature of
the method is the fact that, by exploring the spatial decomposition of
a simplified initial network, one is led to a network of tractable size
in the sense that it is possible to schedule 'K-best' network expansions
in time, represented on a decision graph obtained according to some heuristic
simplifications. For the purpose of defining the network expansions from
the decision graph adequate versions of the K-shortest-paths algorithm
and of a dynamic programming algorithm were used. That is, in ARCOS one
seeks to improve a type of algorithm for primary cable network planning
as presented by Rapp by introducing a new heuristic method that seeks
to optimise the dynamic evolution of the network topology together with
the equipment capacity expansions. The actual version of the ARCOS model
and its application to particular urban networks is described. The advantages
and difficulties of the method are also discussed.}}
@article{Dod-OR-84,
title = {{Determining the $K$ most critical paths in PERT networks}},
author = {Bajis Mohammed Dodin},
journal = {Operations Research},
volume = {32},
pages = {859--877},
year = {1984},
abstract = {A fundamental problem in PERT networks is to identify a project's
critical paths and its critical activities. The author defines the criticality
index of a path as the probability that the duration of the path is greater
than or equal to the duration of every other path in the network and
define the criticality index of an activity as the sum of the criticality
indices of the paths containing that activity. The most critical path
or K most critical paths in a PERT network could be found by enumerating
all the paths and calculating the corresponding criticality indices,
both of which are burdensome tasks. The paper uses stochastic dominance
to develop a procedure to identify the K most critical paths without
using this path enumeration. The procedure has been applied to various
sized PERT networks generated at random, and the results are found to
be very close to those obtained by extensive Monte Carlo sampling.}}
@phdthesis{Dod-PhD-82,
title = {{On the Completion Time of Stochastic PERT Networks}},
author = {Bajis Mohammed Dodin},
school = {North Carolina State Univ., Dept. of Operations Research},
year = {1982},
abstract = {A stochastic PERT network is a directed acyclic network with
$N$ nodes and $A$ arcs, where the arc lengths are independent random
variables with known probability distribution functions. A fundamental
problem in PERT networks is to determine the probability distribution
function (pdf) of the realization time of the project completion time
$T_N$. An equally important problem in PERT networks is to identify the
activities and paths that are critical to the achievement of the project
objectives. Determining the exact pdf of $T_N$ is difficult. In this
thesis we develop two procedures to approximate such pdf's. The first
procedure assumes the independence of the paths in PERT network. It starts
at node 1 and proceeds sequentially to nodes $2, 3, \ldots$, until it
finally reaches node $N$; at each node it approximates the pdf of its
realization time. The second procedure uses the series-parallel decomposition
to reduce the AN to only one activity starting at node 1 and ending in
node $N$. The pdf of the duration of the equivalent activity $(1, N)$
approximates the pdf of the project completion time. In the second problem
if the duration of each activity is constant, then it is relatively easy
to identify the critical path(s) and activities. In contrast such an
identification is very difficult in PERT network. In this dissertation
we first define the concepts of critical path(s) and activities, then
develop procedures to identify the criticality of every activity and
the top $K$ critical paths. To be able to test the accuracy of the approximating
procedures developed in this thesis, a random AN generator was developed
to generate a network $G(N,A)$ at random from the space of all feasible
networks with $N$ nodes and $A$ arcs; also, a crude Monte Carlo sampling
model was developed to approximate the pdf's of the realization times
of every node and the criticality measures of the activities and the
paths. The developed procedures have been programmed and tested using
ANs of sizes $\le G(50, 150)$.}}
@inproceedings{Dre-JNM-68,
title = {{An appraisal of some shortest path algorithms}},
author = {S. E. Dreyfus},
booktitle = {ORSA/TIMS Joint National Mtg.},
journal = {Bull. Operations Research Soc. of America},
volume = {16},
pages = {166},
year = {1968},
abstract = {Abstract only given substantially as follows. Several traditional
problems involving the determination of shortest paths through discrete
networks will be examined. To avoid special cases, it will generally
be assumed that all nodes are directly connected to all other nodes.
Good algorithms will be identified and credited, to the best of the speaker's
knowledge, to their earlier originators. Also some erroneous or inefficient
procedures will be exposed. While little new material is developed, it
is hoped that the talk will shorten some listeners' paths through the
shortest path literature.}}
@article{Dre-OR-69,
title = {{An appraisal of some shortest path algorithms}},
author = {S. E. Dreyfus},
journal = {Operations Research},
volume = {17},
pages = {395--412},
year = {1969}}
@article{DubEpi-ARC-76,
title = {{Search algorithm for optimal alternatives in automated-design
problems}},
author = {Yu. A. Dubov and N. V. Epikhova},
journal = {Automation and Remote Control},
volume = {37},
pages = {1220--1225},
year = {1976},
note = {English translation of \cite{DubEpi-AT-76}}}
@article{DubEpi-AT-76,
title = {{Search algorithm for optimal alternatives in automated-design
problems}},
author = {Yu. A. Dubov and N. V. Epikhova},
journal = {Avtomatika i Telemekhanika},
volume = {37},
pages = {95--100},
year = {1976},
note = {In Russian}}
@article{DunGroMac-JSAC-94,
title = {{Comparison of $k$-shortest paths and maximum flow routing for
network facility restoration}},
author = {D. A. Dunn and Wayne Davy Grover and M. H. MacGregor},
journal = {J. Selected Areas in Communications},
publisher = {IEEE},
volume = {12},
pages = {88--99},
year = {1994},
abstract = {In the development of technologies for span failure restoration,
a question arises about the restoration rerouting characteristics to
be specified. In theory, maximal rerouting capacity is obtained with
a maximum flow (Max Flow) criterion. However, rerouting that realizes
the k-successively shortest link disjoint paths (KSP) may be faster,
easier, and, in distributed implementation, more robust than a distributed
counterpart for Max Flow. The issue is, therefore, what the restoration
capacity penalty is if KSP is used instead of Max Flow. To explore this
tradeoff, the authors present a comparative study of the effectiveness
of KSP versus Max Flow as an alternative rerouting criteria in the context
of transport network span restoration. The comparison applies to both
centrally controlled and distributed restoration systems. Study methods
include exhaustive span failure experiments on a range of network models,
and parametric and analytical investigations for insight into the factors
resulting in KSP versus Max Flow differences. The main finding is that
KSP restoration capacity is more than 99.9{\%} of that from Max Flow in
typical network models. The hypothesis is made that a generalized 'trap'
topology is responsible for all KSP-Max Flow capacity differences. The
hypothesis is tested experimentally and used to develop analytical bounds
which agree well with observed results. These findings and data are relevant
to standards makers and equipment developers in specifying and engineering
future restorable networks.}}
@article{Epp-BIT-92,
title = {{Finding the $k$ smallest spanning trees}},
author = {David Eppstein},
journal = {BIT},
volume = {32},
number = {2},
pages = {237--248},
year = {1992},
review = {MR-94e-05082}}
@article{MR-94e-05082,
reviews = {Epp-BIT-92},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Finding the $k$ smallest spanning trees}},
author = {M. M. Sys{\l}o},
volume = {94e},
number = {05082},
year = {1994},
text = {Improved solutions for the problem of generating the $k$ smallest
spanning trees in a graph and in the plane are presented. The algorithm
for general graphs takes time $O(m\log\beta(m,n)+k\sp 2)$; for planar
graphs this bound can be improved to $O(n+k\sp 2)$.}}
@inproceedings{Epp-FOCS-94,
title = {{Finding the $k$ shortest paths}},
author = {David Eppstein},
booktitle = {Proc. 35th Symp. Foundations of Computer Science},
publisher = {IEEE},
pages = {154--165},
year = {1994}}
@article{Epp-IJCGA-93,
title = {{Tree-weighted neighbors and geometric $k$ smallest spanning trees}},
author = {David Eppstein},
journal = {Int. J. Computational Geometry and Applications},
volume = {4},
number = {2},
pages = {229--238},
year = {1994},
review = {MR-95f-05028}}
@article{MR-95f-05028,
reviews = {Epp-IJCGA-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Tree-weighted neighbors and geometric $k$ smallest spanning trees}},
author = {Ding-Zhu Du},
volume = {95f},
number = {05028},
year = {1995},
text = {Given a set of $n$ points in the plane, construct $k$ different
spanning trees that have the minimum total edge lengths among all possible
spanning trees of the point set. This geometric $k$ smallest spanning
trees problem was proposed by the author previously. In this paper, the
author improves the time bounds for computing the optimal solution. In
particular, the time is $O(n\log n\log k+k(\min(k,n))^{1/2}\log(k/n))$
in the Euclidean plane and $O(n\log n+n\log\log n\log k+k(\min(k,n))^{1/2}\log(k/n))$
in the rectilinear plane.}}
@article{Epp-MER-95,
title = {{Ten algorithms for Egyptian fractions}},
author = {David Eppstein},
journal = {Mathematica in Education and Research},
volume = {4},
number = {2},
pages = {5--15},
year = {1995},
url = {http://www.ics.uci.edu/~eppstein/numth/egypt/},
annote = {Includes an implementation in Mathematica of the algorithm of
Waterman and Byers for listing all paths shorter than a given length
bound \cite{ByeWat-OR-84}, and uses it as a heuristic for the NP-hard
problem of, given a graph with colored edges, finding a shortest path
using each color at most once. This heuristic is used in an algorithm
for finding representations of a rational number as a sum of distinct
unit fractions: the algorithm expands the rational number into a sequence
of unit fractions using continued fractions, finds a graph the edges
of which correspond to subsequences that sum to unit fractions, and forms
the overall representation by finding a path in this graph.}}
@inproceedings{Epp-SWAT-90,
title = {{Finding the $k$ smallest spanning trees}},
author = {David Eppstein},
booktitle = {Proc. 2nd Scandinavian Worksh. Algorithm Theory},
number = {447},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {38--47},
year = {1990}}
@techreport{Epp-TR-92-77,
title = {{Tree-weighted neighbors and geometric $k$ smallest spanning trees}},
author = {David Eppstein},
institution = {Univ. of California, Irvine, Dept. Information and Computer
Science},
number = {92-77},
year = {1992}}
@techreport{Epp-TR-94-26,
title = {{Finding the $k$ shortest paths}},
author = {David Eppstein},
institution = {Univ. of California, Irvine, Dept. Information and Computer
Science},
number = {94-26},
year = {1994}}
@techreport{Epp-TR-95-52,
title = {{Finding common ancestors and disjoint paths in DAGs}},
author = {David Eppstein},
institution = {Univ. of California, Irvine, Dept. Information and Computer
Science},
number = {95-52},
year = {1995},
abstract = {We consider the problem of finding pairs of vertex-disjoint
paths in a DAG, either connecting two given nodes to a common ancestor,
or connecting two given pairs of terminals. It was known how to find
a single pair of paths, for either type of input, in polynomial time.
We show how to find the $k$ pairs with shortest combined length, in time
$O(mn + k)$. We also show how to count all such pairs of paths in $O(mn)$
arithmetic operations. These results can be extended to finding or counting
tuples of $d$ disjoint paths, in time $O(mn^{d-1} + k)$ or $O(mn^{d-1})$.
We give further results on finding the subset of the DAG involved in
pairs of disjoint paths, and on finding disjoint paths in linear space.}}
@inproceedings{EppGalIta-FOCS-92,
title = {{Sparsification -- A technique for speeding up dynamic graph algorithms}},
author = {David Eppstein and Zvi Galil and Giuseppe F. Italiano and Amnon
Nissenzweig},
booktitle = {Proc. 33rd Symp. Foundations of Computer Science},
publisher = {IEEE},
pages = {60--69},
year = {1992},
annote = {The best swap data structure is used to find the $k$ smallest
spanning trees in time $O(m\log\beta(m,n)+kn^{1/2}\log(m/n))$.},
abstract = {The authors provide data structures that maintain a graph as
edges are inserted and deleted, and keep track of the following properties:
minimum spanning forests, best swap, graph connectivity, and graph 2-edge-connectivity,
in time O(n/sup 1/2/log(m/n)) per change; 3-edge-connectivity, in time
O(n/sup 2/3/) per change; 4-edge-connectivity, in time O(n alpha (n))
per change; k-edge-connectivity, in time O(n log n) per change; bipartiteness,
2-vertex-connectivity, and 3-vertex-connectivity, in time O(n log(m/n))
per change; and 4-vertex-connectivity, in time O(n log(m/n)+n alpha (n))
per change. Further results speed up the insertion times to match the
bounds of known partially dynamic algorithms. The algorithms are based
on a technique that transforms algorithms for sparse graphs into ones
that work on any graph, which they call sparsification.}}
@techreport{EppGalIta-IBM-93,
title = {{Sparsification -- A technique for speeding up dynamic graph algorithms}},
author = {David Eppstein and Zvi Galil and Giuseppe F. Italiano and Amnon
Nissenzweig},
institution = {IBM, T. J. Watson Research Ctr.},
number = {RC 19272 (83907)},
year = {1993}}
@article{EppGalIta-JACM-97,
title = {{Sparsification -- A technique for speeding up dynamic graph algorithms}},
author = {David Eppstein and Zvi Galil and Giuseppe F. Italiano and Amnon
Nissenzweig},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {44},
number = {5},
pages = {669--696},
month = {September},
year = {1997},
annote = {This paper combines the FOCS '92 conference version \cite{EppGalIta-FOCS-92}
with the ``Improved Sparsification'' tech. report \cite{EppGalIta-TR-93}.
It includes a ``best swap'' data structure which is used to find the $k$
smallest spanning trees in time $O(M+kn^{1/2})$ (where $M$ denotes the
time to find a single minimum spanning tree in an $m$-edge sparse graph).}}
@techreport{EppGalIta-TR-93,
title = {{Improved sparsification}},
author = {David Eppstein and Zvi Galil and Giuseppe F. Italiano},
institution = {Univ. of California, Irvine, Dept. Information and Computer
Science},
number = {93-20},
year = {1993},
url = {http://www.ics.uci.edu:80/TR/UCI:ICS-TR-93-20},
annote = {The best swap data structure is used to find the $k$ smallest
spanning trees in time $O(m\log\log^*m+k\min(n,k)^{1/2})$.},
abstract = {In previous work we introduced {\em sparsification}, a technique
that transforms fully dynamic algorithms for sparse graphs into ones
that work on any graph, with a logarithmic increase in complexity. In
this work we describe an improvement on this technique that avoids the
logarithmic overhead. Using our improved sparsification technique, we
keep track of the following properties: minimum spanning forest, best
swap, connectivity, 2-edge-connectivity, and bipartiteness, in time $O(n^1/2)$
per edge insertion or deletion; 2-vertex-connectivity and 3-vertex-connectivity,
in time $O(n)$ per update; and 4-vertex-connectivity, in time $O(n\alpha(n))$
per update.}}
@article{FdCGonBas-CABIOS-95,
title = {{A computer program to aid the sequencing of peptides in collision
activated decomposition experiments}},
author = {Jorge Fern{\'a}ndez-de-Coss{\'\i}o and Javier Gonzalez and Vladimir Besada},
journal = {CABIOS: Computer Applications in the Biosciences},
volume = {11},
number = {4},
pages = {427--434},
year = {1995},
abstract = {A computer program named MSEQ, based on the Graph Theory has
been implemented to aid the sequencing of peptides from Collision-Activated
Decomposition (CAD) spectra. Input data required by this program are:
the molecular weight of the peptide, the list of the masses of the daughter
ions and the masses of the N- and C-terminal groups. The output comprises
a list of the most likely sequences with their respective scores and
the assignments of the daughter ions. A set of probabilities for each
fragment ion was computed from hundreds of CAD spectra obtained in our
mass spectrometer. To date many peptides have been sequenced in our laboratory
with the help of this program and, in most of them, the real sequence
ranks among the top five sequences. The program is able to differentiate
isobaric amino acids such as Leucine and Isoleucine when the side-chain
fragmentation appears in the spectrum. A criterion is used to discard
those sequences that match the spectrum poorly from the earliest steps.
The program is fast and no memory consuming.}}
@article{FdCGonBet-RCMS-98,
title = {{Automated interpretation of high-energy collision-induced dissociation
spectra of singly protonated peptides by SeqMS, a software aid for de
novo sequencing by tandem mass spectrometry}},
author = {Jorge Fern{\'a}ndez-de-Coss{\'\i}o and Javier Gonzalez and Luis Betancourt
and Vladimir Besada and Gabriel Padron and Yasutsugu Shimonishi and Toshifumi
Takao},
journal = {Rapid Communications in Mass Spectrometry},
volume = {12},
number = {23},
pages = {1867--1878},
year = {1998}}
@inproceedings{Fen-SIPPN-94,
title = {{Applying $N$-best keyword search to continuous speech recognition
for telecommunication-based applications}},
author = {Ming-Whei Feng},
booktitle = {Proc. Int. Symp. Speech, Image Processing, and Neural Networks},
publisher = {IEEE},
volume = {2},
pages = {726--729},
month = {April},
year = {1994},
abstract = {An $N$-best keyword search algorithm was developed in a continuous
speech recognizer which models vocabulary words as well as extraneous
sounds and noise, to achieve high sentence accuracy. The continuous speech
recognizer was developed for telecommunication-based applications which
typically demand high sentence accuracy. Possible approaches for achieving
high sentence accuracy include applying complicated speech modeling techniques
or employing more knowledge sources when conducting the recognition search.
An alternative solution is to first apply an $N$-best decoding search
to obtain $N$ sentence hypotheses using pre-selected knowledge source(s)
and then re-score those hypotheses using other knowledge source(s) or
models. The proposed $N$-best keyword search algorithm derives all keyword
sentence hypotheses and the corresponding likelihood scores time-synchronously.
We show that the algorithm guarantees to find all sentence hypotheses.
To reduce the exponentially growing number of hypotheses, in practical
implementation we applied empirically derived thresholds to prune the
search. Recognition experiments were conducted on two speech corpora:
TI Connected Digit Corpus and Road Rally Corpus, to show the effectiveness
of the proposed method.}}
@misc{Fok-96,
title = {{Library for finding the $K$ shortest paths in a graph}},
author = {Kenny K. Y. Fok},
howpublished = {Univ. Waterloo, CS648 Course Project},
year = {1996},
url = {http://mercator.uwaterloo.ca/~kykfok/ps/cs648paper.ps},
month = {Spring}}
@book{ForFul-62,
title = {{Flows in Networks}},
author = {Ford, Jr., Lester R. and D. R. Fulkerson},
address = {Princeton, NJ},
publisher = {Princeton Univ. Press},
year = {1962}}
@article{Fox-CACM-75,
title = {{More on $k$th shortest paths}},
author = {B. L. Fox},
journal = {Commun. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {18},
number = {5},
pages = {279},
month = {May},
year = {1975},
text = {In a recent paper \cite{Min-CACM-74}, Minieka proposes an algorithm
for finding $k$th shortest paths between all pairs of nodes in an $N$
node network. His claimed time is $O(k^2N^3)$.
Fox \cite{Fox-INFOR-73} applies HEAPSORT \cite{Wil-CACM-64} to the Hoffman-Pavley-Dreyfus
algorithm \cite{Dre-OR-69} for finding $K$th shortest paths to a given
node. Applying this algorithm $N$ times finds the $k$th shortest paths
between all pairs of nodes in time $O(kN^2\log N + N^3\log N)$. For large
$k$, this is an order of magnitude faster.
Fox \cite{Fox-INFOR-73} also introduced a perturbation scheme that eliminates
bookkeeping due to ties and eliminates the possibility of cycling on
zero-length loops. The latter is important in integer programming applications.
Fox showed how to (easily) recover the solution to the original problem.
For the case $k=1$, the papers of Spira \cite{Spi-SJC-73} and Hoffman
and Winograd \cite{HofWin-IBMJRD-72} should be mentioned.}}
@article{Fox-INFOR-73,
title = {{Calculating $k$th shortest paths}},
author = {B. L. Fox},
journal = {INFOR--Canad. J. Op. Res. {\&} Inf. Proc.},
volume = {11},
pages = {66--70},
year = {1973}}
@inproceedings{Fox-JNM-75,
title = {{$k$-th shortest paths and applications to the probabilistic networks}},
author = {B. L. Fox},
booktitle = {ORSA/TIMS Joint National Mtg.},
journal = {Bull. Operations Research Soc. of America},
volume = {23},
pages = {B263},
year = {1975},
abstract = {Shows how to calculate k-th shortest paths to a given node
in a n-node network in time O(n(klogn+n)). In acyclic networks (e.g.
PERT networks) such paths are automatically loopless. Some heuristic
applications to networks with random arc lengths are mentioned.}}
@article{Fox-OR-78,
title = {{Data structures and computer science techniques in operations
research}},
author = {B. L. Fox},
journal = {Operations Research},
volume = {26},
pages = {686--717},
year = {1978}}
@article{FraMon-Nw-75,
title = {{A vertex elimination algorithm for enumerating all simple paths
in a graph}},
author = {L. Fratta and Ugo Montanari},
journal = {Networks},
volume = {5},
number = {2},
pages = {151--177},
month = {April},
year = {1975},
abstract = {If a suitable definition of sum and multiplication between
sets of paths is given, the sets of all simple paths between all pairs
of vertices in a graph can be characterized as the solution of a system
of linear equations. The well-known matrix technique for enumerating
such paths corresponds to an iterative solution of this system. A new
and more efficient algorithm is here described and analyzed which finds
all simple paths by a vertex elimination technique similar to Jordan's
method for matrix inversion. Experimental results about a FORTRAN implementation
of the algorithm are finally reported.}}
@inproceedings{Fre-FOCS-91,
title = {{Ambivalent data structures for dynamic 2-edge-connectivity and
$k$ smallest spanning trees}},
author = {Greg N. Frederickson},
booktitle = {Proc. 32nd Symp. Foundations of Computer Science},
publisher = {IEEE},
pages = {632--641},
year = {1991},
review = {MR-93i-68043}}
@article{MR-93i-68043,
reviews = {Fre-FOCS-91},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Ambivalent data structures for dynamic 2-edge-connectivity and
$k$ smallest spanning trees}},
volume = {93i},
number = {68043},
year = {1993},
text = {Ambivalent data structures are presented for several problems on
undirected graphs. They are used in finding the $k$ smallest spanning
trees of a weighted undirected graph in $O(m\log\beta(m,n)+\min\{k\sp
{3/2},km\sp {1/2}\})$ time, where $m$ is the number of edges and $n$
the number of vertices in the graph. The techniques are extended to find
the $k$ smallest spanning trees in an embedded planar graph in $O(n+k(\log
n)\sp 3)$ time. Ambivalent data structures are also used to maintain
dynamically 2-edge-connectivity information. Edges and vertices can be
inserted or deleted in $O(m\sp {1/2})$ time, and a query as to whether
two vertices are in the same 2-edge-connected component can be answered
in $O(\log n)$ time, where $m$ and $n$ are understood to be the current
number of edges and vertices, respectively. Again, the techniques are
extended to maintain an embedded planar graph so that edges and vertices
can be inserted or deleted in $O((\log n)\sp 3)$ time, and a query answered
in $O(\log n)$ time.}}
@article{Fre-IC-93,
title = {{An optimal algorithm for selection in a min-heap}},
author = {Greg N. Frederickson},
journal = {Information and Computation},
volume = {104},
pages = {197--214},
year = {1993},
review = {MR-94m-68030}}
@article{MR-94m-68030,
reviews = {Fre-IC-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An optimal algorithm for selection in a min-heap}},
author = {Vijay V. Raghavan},
volume = {94m},
number = {68030},
year = {1994},
text = {Selecting the $k$th smallest element in a set is an important problem
in order statistics. An optimal algorithm for this problem exists [M.
Blum et al., J. Comput. System Sci. 7 (1973), 448--461; MR 48 {\#}8256].
The present paper considers the problem of finding the $k$th smallest
element in a set of elements satisfying a partial order relation. A convenient
way to organize the elements of a set for this purpose is to consider
a binary min-heap, i.e. a partial order on the elements $x\sb i$, $i=1,2,\cdots,n$,
where $x\sb i>x\sb {\lfloor i/2\rfloor}$. In order to achieve a simple
upper bound of $O(k\log k)$, the $k$ smallest elements in the set are
extracted via an auxiliary heap. The auxiliary heap is used to hold those
elements that are candidates for being the next smallest elements.
In improving on the above bound, the elements in the set are grouped
into clans of equal size. By identifying groups of elements and using
the largest in the group, it is possible to reduce the complexity of
operation on the auxiliary heap. The largest of the largest element in
each clan serves as a bound on the $k$ smallest elements in the set and
is used to extract the subset of elements from which the $k$th smallest
is selected. An algorithm using the idea of clans is discussed for the
general problem of finding the $k$th smallest element in a forest of
heaps.
Under a different strategy, the clans are redefined to consist of all
the elements of smaller clans, with the lowest-level clans having the
single smallest element. This allows the heap structure to represent
clans as they are organized bottom-up in an incremental fashion. By keeping
the size of a clan as small as necessary at any given time, the author
provides an algorithm with time complexity $O(k)$.
This result represents an optimal algorithm for the problem of selecting
the $k$th smallest element in a set organized as a binary heap, since
the information-theoretic lower bound is known to be $\Omega(k)$ [D.
E. Knuth, The art of computer programming, Volume I, second edition,
Addison-Wesley, Reading, MA, 1975; MR 51 {\#}14624]. This is an important
result, particularly from a theoretical perspective. The general problem
of selecting the $k$th smallest element in a set has many applications.
The author cites two example applications where the set of elements is
easily viewed as a binary heap: (i) enumeration of the $k$ smallest spanning
trees of a weighted undirected graph [G. N. Frederickson, in 32nd Annual
Symposium on Foundations of Computer Science (San Juan, PR, 1991), 632--641,
IEEE Comput. Soc. Press,
Los Alamitos, CA, 1991; MR 93i:68043] and (ii) the tree-structured resource
allocation problem [T. Ibaraki and N. Katoh, Resource allocation problems,
MIT Press, Cambridge, MA, 1988; MR 89e:90179]. He notes that in both
cases it is possible to improve efficiency by using his algorithm.}}
@article{Fre-SJC-85,
title = {{Data structures for on-line updating of minimum spanning trees,
with applications}},
author = {Greg N. Frederickson},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {14},
number = {4},
pages = {781--798},
year = {1985},
review = {MR-86m-68121}}
@article{MR-86m-68121,
reviews = {Fre-SJC-85},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Data structures for on-line updating of minimum spanning trees,
with applications}},
volume = {86m},
number = {68121},
year = {1986},
text = {Data structures are presented for the problem of maintaining an
on-line minimum spanning tree under the operation of updating the cost
of some edge in the graph. For the case of a general graph, maintaining
the data structure and updating the tree are shown to take $O(\sqrt{m})$
time, where $m$ is the number of edges in the graph. For the case of
a planar graph, a data structure is presented which supports an update
time of $O((\log m)\sp 2)$. These structures contribute to improved solutions
for the on-line connection components problem and the problem of generating
the $K$ smallest spanning trees.}}
@article{Fre-SJC-97,
title = {{Ambivalent data structures for dynamic 2-edge-connectivity and
$k$ smallest spanning trees}},
author = {Greg N. Frederickson},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {26},
number = {2},
pages = {484--538},
month = {April},
year = {1997}}
@article{FreJoh-Algs-83,
title = {{Finding $k$th paths and $p$-centers by generating and searching
good data structures}},
author = {Greg N. Frederickson and Donald B. Johnson},
journal = {J. Algorithms},
volume = {4},
pages = {61--80},
year = {1983},
abstract = {A succinct and easily searchable representation of the set
of intervertex distances of a tree is given. Algorithms are presented
for generating this representation, for searching it to select a kth
longest path, and for searching it to locate a p-center. The complete
algorithm for path selection is asymptotically optimal in the worst case,
and the algorithms for p-center location improve on previous methods.
The p-center results are extended to networks with independent cycles.}}
@article{FreTar-JACM-87,
title = {{Fibonacci heaps and their uses in improved network optimization
algorithms}},
author = {Michael L. Fredman and Robert E. Tarjan},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {34},
pages = {596--615},
year = {1987},
abstract = {The authors develop a new data structure for implementing heaps
(priority queues). The structure, Fibonacci heaps (abbreviated F-heaps),
extends the binomial queues. F-heaps support arbitrary detection from
an $n$-item heap in $O(\log{n})$ amortized time and all other standard
heap operations in $O(1)$ amortized time. Using F-heaps they are able
to obtain improved running times for several network optimization algorithms.
In particular, they obtain the following worst-case bounds, where $n$
is the number of vertices and m the number of edges in the problem graph:
(1) $O(n\log{n}+m)$ for the single-source shortest path problem with
nonnegative edge lengths, improved from $O(m\log_{m/n+2}{n})$; (2) $O(n^2\log{n}+nm)
for the all-pairs shortest path problem, improved from $O(nm\log_{m/n+2}{n})$;
(3) $O(n{$^\wedge$}2\log{n}+nm)$ for the assignment problem (weighted bipartite
matching), improved from $O(nm\log_{m/n+2}{n})$; (4) $O(m\beta(m,n))$
for the minimum spanning tree problem, improved from $O(m\log\log_{m/n+2}{n})$,
where $\beta(m,n)=min\{i\mid\log{$^\wedge$}{(i)}{n}\le m/n\}$. Note that $\beta(m,n)\le\log{$^\wedge$}*{n}$
if $m\ge n$. Of these results, the improved bound for minimum spanning
trees is the most striking, although all the results give asymptotic
improvements for graphs of appropriate densities.}}
@inproceedings{FreWil-FOCS-90,
title = {{Trans-dichotomous algorithms for minimum spanning trees and shortest
paths}},
author = {Michael L. Fredman and Dan E. Willard},
booktitle = {Proc. 31st Symp. Foundations of Computer Science},
publisher = {IEEE},
pages = {719--725},
year = {1990},
abstract = {Two algorithms are presented: a linear time algorithm for the
minimum spanning tree problem and an $O(m+n\log{n}/\log\log{n})$ implementation
of Dijkstra's shortest-path algorithm for a graph with $n$ vertices and
$m$ edges. The second algorithm surpasses information theoretic limitations
applicable to comparison-based algorithms. Both algorithms utilize new
data structures that extend the fusion tree method.}}
@inproceedings{Fuc-ORP-84,
title = {{$1$-$n$ Verfahren zur Bestimmung von $k$-kurzesten Wegen}},
author = {Alois Fuchs},
booktitle = {Operations Research Proceedings},
publisher = {Springer Verlag},
pages = {421--428},
year = {1984}}
@article{FukMat-Nw-92,
title = {{Finding all minimum-cost perfect matchings in bipartite graphs}},
author = {Komei Fukuda and Tomomi Matsui},
journal = {Networks},
volume = {22},
number = {5},
pages = {461--468},
year = {1992},
review = {MR-93c-05104}}
@article{MR-93c-05104,
reviews = {FukMat-Nw-92},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Finding all minimum-cost perfect matchings in bipartite graphs}},
volume = {93c},
number = {05104},
year = {1993},
text = {The Hungarian method is an efficient algorithm for finding a minimal-cost
perfect matching in a weighted bipartite graph. We describe an efficient
algorithm for finding all minimal-cost perfect matchings. The computational
time required to generate each additional perfect matching is $O(n(n+m))$,
and it requires $O(n+m)$ memory storage. This problem can be solved by
algorithms for finding the $K$th-best solution of assignment problems.
However, the memory storage required by the known algorithms grows in
proportion to $K$, and, hence, it may grow exponentially in $n$. Thus,
our specialized algorithm has a considerable advantage in memory requirement
over the previous more general algorithms for $K$th-best assignment problems.
Here we show that the enumeration of all minimal-cost perfect matchings
can be reduced to the enumeration of all perfect matchings in some bipartite
graph. Therefore, our algorithm can be seen as an algorithm for enumerating
all perfect matchings in a given bipartite graph.}}
@article{FuRil-TRB-98,
title = {{Expected shortest paths in dynamic and stochastic traffic networks}},
author = {Liping Fu and L. R. Rilett},
journal = {Transportation Research, Part B. -- Methodological},
volume = {32B},
number = {7},
pages = {499--416},
month = {September},
year = {1998},
abstract = {The dynamic and stochastic shortest path problem (DSSPP) is
defined as finding the expected shortest path in a traffic network where
the link travel times are modeled as a continuous-time stochastic process.
The objective of the paper is to examine the properties of the problem
and to identify a technique that can be used to solve the DSSPP given
information that will be available in networks with intelligent transportation
system (ITS) capabilities. The paper first identifies a set of relationships
between the mean and variance of the travel time of a given path and
the mean and variance of the dynamic and stochastic link travel times
on these networks. Based on these relationships it is shown that the
DSSPP is computationally intractable and traditional shortest path algorithms
cannot guarantee an optimal solution. A heuristic algorithm based on
the k-shortest path algorithm is subsequently proposed to solve the problem.
Lastly, the trade-off between solution quality and computational efficiency
of the proposed algorithm is demonstrated on a realistic network from
Edmonton, Alberta.}}
@inproceedings{FuRil-VNIS-95,
title = {{Estimation of expected minimum paths in dynamic and stochastic
traffic networks}},
author = {Liping Fu and L. R. Rilett},
booktitle = {Proc. 6th Int. Conf. Vehicle Navigation and Information Systems},
publisher = {IEEE},
pages = {200--205},
year = {1995},
abstract = {For most in-vehicle route guidance systems (RGS) currently
under development, the optimal route between an origin and destination
is defined as the one with the minimum expected travel time. This optimal
route is calculated by applying standard shortest path algorithms to
the network where the link travel times are modeled as deterministic
rather than as stochastic. The drawback to this method is that while
it is computationally tractable, it may, in fact, generate a sub-optimal
solution. Conversely, when the stochastic nature of link travel times
are explicitly modeled, an optimal algorithm can become computationally
inefficient for use within an actual application. The objective of this
paper is to develop a new shortest path algorithm which takes into account
the stochastic nature of link travel times without significantly increasing
the overall computation time. The dynamic and stochastic shortest path
problem (DSSPP) is first defined and the properties associated with this
problem are discussed. A heuristic algorithm based on the k-shortest
path algorithm is subsequently proposed. The trade-off between solution
quality and computational efficiency of the proposed algorithm will be
demonstrated on a network from Edmonton, Alberta, Canada.}}
@article{Gab-SJC-77,
title = {{Two algorithms for generating weighted spanning trees in order}},
author = {Harold N. Gabow},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {6},
pages = {139--150},
year = {1977}}
@article{GarBer-Cyb-79,
title = {{Determination of the paths in an oriented acyclical graph}},
author = {S. I. Garkavenko and L. S. Berdnikova},
journal = {Cybernetics},
volume = {15},
number = {4},
pages = {489--493},
month = {July},
year = {1979},
abstract = {Gives a fairly easily programmed method for finding all the
paths in an acyclical graph. As a preliminary, the vertices are renumered,
then, from the incidence matrix of the graph with renumbered vertices,
the matrix of paths is constructed. The rows of the latter matrix represent
all the paths between the inputs and outputs.}}
@book{GarJoh-79,
title = {{Computers and Intractability: a Guide to the Theory of NP-Completeness}},
author = {Michael R. Garey and David S. Johnson},
publisher = {W. H. Freeman},
year = {1979}}
@article{Gav-Algs-87,
title = {{Generating the maximum spanning-trees of a weighted graph}},
author = {Fanica Gavril},
journal = {J. Algorithms},
volume = {8},
number = {4},
pages = {592--597},
month = {December},
year = {1987}}
@article{Gol-SJC-95,
title = {{Scaling algorithms for the shortest paths problem}},
author = {Andrew V. Goldberg},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {24},
number = {3},
pages = {494--504},
month = {June},
year = {1995}}
@inproceedings{Gol-SODA-93,
title = {{Scaling algorithms for the shortest paths problem}},
author = {Andrew V. Goldberg},
booktitle = {Proc. 4th Symp. Discrete Algorithms},
publisher = {ACM and SIAM},
pages = {222--231},
month = {January},
year = {1993}}
@inproceedings{GouPraAbu-ETWCS-99,
title = {{Routing in LEO-based satellite networks.}},
author = {V. V. Gounder and Ravi Prakash and H. Abu-Amara},
booktitle = {Proc. Emerging Technologies Symp. Wireless Communications
and Systems},
publisher = {IEEE},
month = {April},
year = {1999},
url = {http://www.utdallas.edu/~ravip/papers/ets99.satellite.ps}}
@inproceedings{GrnKleGer-CNS-79,
title = {{A new algorithm for network reliability computation}},
author = {A. Grnarov and L. Kleinrock and M. Gerla},
booktitle = {Proc. Computer Networking Symp.},
publisher = {IEEE},
pages = {17--20},
month = {December},
year = {1979},
abstract = {A new algorithm for terminal reliability computation of a general
network is presented. The algorithm belongs to the path enumeration algorithms
(which use Boolean algebra) and is based on performing the here defined
\$-operation (modified no.operation) on the set of all simple paths.}}
@phdthesis{Gro-PhD-89,
title = {{Selfhealing networks: a distributed algorithm for $k$-shortest
link-disjoint paths in a multi-graph with applications in real-time network
restoration}},
author = {Wayne Davy Grover},
school = {Univ. of Alberta, Dept. of Electrical Engineering},
year = {1989},
month = {Fall}}
@inproceedings{GroVen-ICC-91,
title = {{Performance of the Selfhealing Network protocol with random individual
link failure times}},
author = {Wayne Davy Grover and B. D. Venables},
booktitle = {Proc. Int. Conf. Communications (ICC '91)},
publisher = {IEEE},
volume = {2},
pages = {660--666},
year = {1991},
abstract = {The Selfhealing Network (SHN) is a parallel asynchronous distributed
protocol which organizes the pool of spare links in a network into the
pattern of k-shortest link disjoint paths between any two nodes of the
network. A report is presented on the behavior of the SHN protocol when
presented with a random series of individual fiber failures, as opposed
to a 'guillotine' (i.e. simultaneous) model of a cable cut. The most
significant results are: (a) verification of the protocol under complex
failure stimuli, and (b) a finding of predeployment effects which reduce
the elapsed outage time of most individual paths when failures occur
in a time-distributed manner.}}
@article{GuaChe-KT-85,
title = {{A simple algorithm for finding the second order-constrained base
of matroid}},
author = {Mei Gu Guan and Qing Hua Chen},
journal = {Kexue Tongbao (English Ed.)},
volume = {30},
number = {7},
pages = {862--865},
year = {1985},
review = {MR-86m-05030}}
@article{MR-86m-05030,
reviews = {GuaChe-KT-85},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A simple algorithm for finding the second order-constrained base
of matroid}},
author = {Ulrich Wolfgang Faigle},
volume = {86m},
number = {05030},
year = {1986},
text = {The authors propose an algorithm to solve the following problem:
among all bases of a matroid which intersect a given subset in exactly
$k$ elements, find one with the second best possible weight.}}
@inproceedings{GueLacMus-AIRO-96,
title = {{Una classe di algoritmi a correzione di contrassegno per il problema
dei $K$ cammini minimi senza cicli}},
author = {Francesca Guerriero and Valerio Lacagnina and Roberto Musmanno
and Antonio Pecorella},
booktitle = {Proc. AIRO 1996},
publisher = {Associazione Italiana Ricerca Operativa},
pages = {163--166},
year = {1996}}
@article{GueMus-JOTA-00,
title = {{Parallel asynchronous algorithms for the $K$ shortest paths problem}},
author = {Francesca Guerriero and Roberto Musmanno},
journal = {J. Optimization Th. {\&} Appl.},
volume = {104},
number = {1},
pages = {91--108},
month = {January},
year = {2000}}
@techreport{GueMus-TR-96,
title = {{Label-setting methods for the $K$ shortest paths problem}},
author = {Francesca Guerriero and Roberto Musmanno},
institution = {Univ. of Calabria, Dept. of Electronics, Informatics and
Systems},
number = {PARCOLAB 9/96},
month = {December},
year = {1996}}
@inproceedings{GuoMat-ICDCS-99,
title = {{Search space reduction in QoS routing}},
author = {Liang Guo and I. Matta},
booktitle = {Proc. 19th Int. Conf. Distributed Computing Systems},
publisher = {IEEE},
editor = {M. G. Gouda},
pages = {142--149},
month = {May},
year = {1999},
abstract = {To provide real time service, integrated networks require the
underlying routing algorithm to be able to find low cost paths that satisfy
given Quality of Service (QoS) constraints. The problem of constrained
shortest (least cost) path routing is known to be NP hard, and some heuristics
have been proposed to find a near optimal solution. However, these heuristics
either impose relationships among the link metrics to reduce the complexity
of the problem which may limit the general applicability of the heuristic,
or are too costly in terms of execution time to be applicable to large
networks. We focus on solving the delay constrained minimum cost path
problem, and present a fast algorithm to find a near optimal solution.
This algorithm, called DCCR (Delay-Cost-Constrained Routing), is a variant
of the k-shortest path algorithm. DCCR uses a new adaptive path weight
function, together with an additional constraint imposed on the path
cost, to restrict the search space. Thus, DCCR can return a near optimal
solution in a very short time. Furthermore, we use the method proposed
by D. Blokh and G. Gutin (1995) to further reduce the search space by
using a tighter bound on path cost. This makes our algorithm more accurate
and even faster. We call this improved algorithm SSR+DCCR (Search Space
Reduction+DCCR). Through extensive simulations, we confirm that SSR+DCCR
performs very well compared to the optimal but very expensive solution.}}
@article{HadChr-Nw-99,
title = {{An efficient implementation of an algorithm for finding $K$ shortest
simple paths}},
author = {E. Hadjiconstantinou and Nicos Christofides},
journal = {Networks},
volume = {34},
number = {2},
pages = {88--101},
month = {September},
year = {1999}}
@incollection{HadChrMin-AOR-95,
title = {{A new exact algorithm from the vehicle routing problem based
on $q$-paths and $k$-shortest paths relaxations}},
author = {Eleni Hadjiconstantinou and Nicos Christofides and Aristide Mingozzi},
booktitle = {Freight Transportation},
number = {61},
editor = {G. Laporte and Michel Gendreau},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
pages = {21--44},
year = {1995},
review = {MR-96j-90028}}
@article{MR-96j-90028,
reviews = {HadChrMin-AOR-95},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A new exact algorithm from the vehicle routing problem based
on $q$-paths and $k$-shortest paths relaxations}},
volume = {96j},
number = {90028},
year = {1996},
text = {We consider the basic vehicle routing problem (VRP) in which a
fleet of $M$ identical vehicles stationed at a central depot is to be
optimally routed to supply customers with known demands subject only
to vehicle capacity constraints. In this paper, we present an exact algorithm
for solving the VRP that uses lower bounds obtained from a combination
of two relaxations of the original problem which are based on the computation
of $q$-paths and $k$-shortest paths. A set of reduction tests derived
from the computation of these bounds is applied to reduce the size of
the problem and to improve the quality of the bounds. The resulting lower
bounds are then embedded into a tree-search procedure to solve the problem
optimally. Computational results are presented for a number of problems
taken from the literature. The results demonstrate the effectiveness
of the proposed method in solving problems involving up to about 50 customers
and in proving tight lower bounds for problems up to about 150 customers.}}
@book{Hae-LAMM-79,
title = {{Graphentheoretische Methoden des Operations Research}},
author = {Kurt H{\"a}ssig},
series = {Leitf{\"a}den der Angewandten Mathematik und Mechanik},
publisher = {B. G. Teubner},
number = {42},
year = {1979},
review = {MR-80f-90002}}
@article{MR-80f-90002,
reviews = {Hae-LAMM-79},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Graphentheoretische Methoden des Operations Research}},
author = {Rainer E. Burkard},
volume = {80f},
number = {90002},
year = {1980},
text = {The author considers the two main graph-theoretic tools in operations
research: distance and flow problems. The definitions and concepts of
graph theory which are used subsequently are introduced in the first
chapter. In many cases the definitions are followed by algorithms which
solve the corresponding graph-theoretic problems (e.g., determination
of a rooted tree, determination of the strong components of a graph,
etc.). In the theoretical part of the second chapter the following problems
are discussed and algorithmically solved: shortest path problems, determination
of paths with maximal length, determination of negative circuits, and
k-shortest path problems. A detailed presentation of applications is
given for the solution of scheduling problems by means of network-planning.
These are considered in the third chapter. CPM, PERT and MPM, which are
algorithms to solve such problems, are shown to be special cases of the
methods described in Chapter 2. In Chapter 4, flow and tension problems
are solved: algorithms for the determination of maximal flows and flows
with minimal costs, minimal tensions and tensions with minimal costs
are described. As an application, multicommodity flows are solved by
a decomposition algorithm. If the incidence matrix of a graph is replaced
by a generalized incidence matrix one can formulate generalized flow
and tension problems. Algorithms for solving these problems have been
developed by the author and are presented in the fifth chapter. In the
last chapter, the author discusses the travelling- salesman problem,
the matching-problem, and the Chinese-postman problem. The book contains
several examples which clarify the presented theory and applications.}}
@incollection{Ham-AOR-95,
title = {{A note on $K$ best network flows}},
author = {Horst W. Hamacher},
booktitle = {Mathematics of Industrial Systems},
number = {57},
editor = {Rainer E. Burkard and Toshihide Ibaraki and Maurice Queyranne},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
pages = {65--72},
month = {June},
year = {1995},
review = {MR-96d-90027}}
@article{MR-96d-90027,
reviews = {Ham-AOR-95},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A note on $K$ best network flows}},
volume = {96d},
number = {90027},
year = {1996},
text = {It is shown that the problem of finding the $K$ best solutions
of a linear integer network flow problem can be solved by a polynomial
time algorithm. This algorithm can be used in order to solve a multiple-criteria
network flow problem which minimizes the maximum of $Q$ objectives.}}
@incollection{HamPicQue-ACMOR-84,
title = {{Ranking the cuts and cut-sets of a network}},
author = {Horst W. Hamacher and Jean-Claude Picard and Maurice Queyranne},
booktitle = {Algebraic and Combinatorial Methods in Operations Research},
number = {95},
series = {Math. Stud.},
publisher = {North-Holland},
pages = {183--200},
year = {1984},
review = {MR-87b-90135}}
@article{MR-87b-90135,
reviews = {HamPicQue-ACMOR-84},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Ranking the cuts and cut-sets of a network}},
volume = {87b},
number = {90135},
year = {1987},
text = {The authors present an $O(Kn\sp 4)$ algorithm for finding the $K$
best cuts and an $O(m\sp {K-1}n\sp 3)$ algorithm for finding the $K$
best cut-sets in a network with $n+2$ nodes and $m$ arcs.}}
@article{HamPicQue-ORL-84,
title = {{On finding the $K$ best cuts in a network}},
author = {Horst W. Hamacher and Jean-Claude Picard and Maurice Queyranne},
journal = {Operations Research Lett.},
volume = {2},
number = {6},
pages = {303--305},
year = {1984},
review = {MR-85b-90026}}
@article{MR-85b-90026,
reviews = {HamPicQue-ORL-84},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On finding the $K$ best cuts in a network}},
volume = {85b},
number = {90026},
year = {1985},
text = {We show that the $O(K\cdot n\sp 4)$ algorithm of Hamacher (1982)
for finding the $K$ best cut-sets fails because it may produce cuts rather
than cut-sets. With the convention that two cuts $(X, \bar X)$ and $(Y,
\bar Y)$ are different whenever $X\ne Y$ the $K$ best cut problem can
be solved in $O(K\cdot n\sp 4)$.}}
@incollection{HamQue-AOR-85,
title = {{$K$ best solutions to combinatorial optimization problems}},
author = {Horst W. Hamacher and Maurice Queyranne},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
number = {4},
pages = {123--143},
year = {1985},
review = {MR-89b-90174}}
@article{MR-89b-90174,
reviews = {HamQue-AOR-85},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{$K$ best solutions to combinatorial optimization problems}},
volume = {89b},
number = {90174},
year = {1989},
text = {We review the Lawler-Murty procedure for finding the $K$ best solutions
to combinatorial optimization problems. Then we introduce an alternative
algorithm which is based on a binary search tree procedure. We apply
both algorithms to the problems of finding the $K$ best bases in a matroid,
perfect matchings, and best cuts in a network.}}
@incollection{HamRuh-AOR-94,
title = {{On spanning tree problems with multiple objectives}},
author = {Horst W. Hamacher and G{\"u}nter Ruhe},
booktitle = {Decision Theory and Systems},
number = {52},
editor = {K. Mosler and M. Schader},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
pages = {209--230},
year = {1994},
review = {MR-95g-90062}}
@article{MR-95g-90062,
reviews = {HamRuh-AOR-94},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On spanning tree problems with multiple objectives}},
author = {Roman Slowinski},
volume = {95g},
number = {90062},
year = {1995},
text = {Two versions of multiple objective minimum spanning tree problems
defined on a network with vectorial weights are investigated. First,
the maximum of $Q$ linear objective functions taken over the set of all
spanning trees (max-linear spanning tree problem, ML-ST) is considered.
Secondly, efficient spanning trees (multi-criteria spanning tree problem,
MC-ST) are sought. Problem ML-ST is shown to be NP-complete. An exact
algorithm which is based on ranking is presented. The procedure can also
be used as an approximation scheme. For solving the bicriterion MC-ST,
which in the worst case may have an exponential number of efficient trees,
a two-phase procedure is presented. Based on the computation of extremal
efficient spanning trees the neighbourhood search is used to determine
a sequence of solutions with the property that the distance between two
consecutive solutions is less than a given accuracy.}}
@article{HanJauDeA-EJOR-98,
title = {{Mixed-integer column generation algorithms and the probabilistic
maximum satisfiability problem}},
author = {P. Hansen and B. Jaumard and De Aragao, M. P.},
journal = {Eur. J. Operational Research},
volume = {108},
number = {3},
pages = {671--683},
month = {August},
year = {1998},
abstract = {The column generation approach to large-scale linear programming
is extended to the mixed-integer case. Two general algorithms, a dual
and a primal one, are presented. Both involve finding k-best solutions
to combinatorial optimization subproblems. Algorithms for these subproblems
must be tailored to each specific application. Their use is illustrated
by applying them to a new combinatorial optimization problem with applications
in artificial intelligence: probabilistic maximum satisfiability. This
problem is defined as follows: consider a set of logical sentences together
with probabilities that they are true, assume this set of sentences is
not satisfiable in the probabilistic sense, i.e., there is no probability
distribution on the set of possible worlds (truth assignments to the
sentences corresponding to at least one truth assignment to the logical
variables they contain) such that for each sentence the sum of probabilities
of the possible worlds in which it is true is equal to its probability
of being true; determine a minimum set of sentences to be deleted in
order to make the remaining set of sentences satisfiable. Computational
experience with both algorithms is reported on.}}
@article{HanZan-Nw-80,
title = {{A dual algorithm for the constrained shortest path problem}},
author = {Gabriel Y. Handler and Israel Zang},
journal = {Networks},
volume = {10},
number = {4},
pages = {293--309},
year = {1980},
abstract = {Develops a Lagrangian relaxation algorithm for the problem
of finding a shortest path between two nodes in a network, subject to
a knapsack-type constraint. For example, one may wish to find a minimum
cost route subject to a total time constraint in a multimode transportation
network. Furthermore, the problem, which is shown to be at least as hard
as NP-complete problems, is generic to a class of problems that arise
in the solution of integer linear programs and discrete state/stage deterministic
dynamic programs. One approach to solving the problem is to utilize a
kth shortest path algorithm, terminating with the first path that satisfies
the constraint. This approach is impractical when the terminal value
of k is large. Using Lagrangian relaxation the authors propose a method
that is designed to reduce this value of k. Computational results indicate
orders of magnitude savings when the approach is applied to large networks.}}
@inproceedings{HarKapKum-WADS-95,
title = {{Faster enumeration of all spanning trees of a directed graph}},
author = {R. Hariharan and Sanjiv Kapoor and V. Kumar},
booktitle = {Proc. 4th Worksh. Algorithms {\&} Data Structures},
number = {955},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {428--439},
year = {1995},
note = {We present an algorithm for enumerating all spanning trees of a
directed graph with V vertices, E edges and N spanning trees. The algorithm
takes O(log V) time per spanning tree; more precisely, it runs in O(N
log V + V-2 alpha(V, V)+ V E) time(4). It first outputs a single spanning
tree and then a list of edge swaps; each spanning tree can be generated
from the first spanning tree by applying a prefix of this sequence of
edge swaps. The total output size is O(N) as against the O(NV) size of
all spanning trees put together. The previous best known algorithm for
this problem [KR91] took O(NV + V-3) time, even for generating the edge
swap sequence.}}
@inproceedings{HatKni-IJCAI-95,
title = {{Unification-based glossing}},
author = {Vasileios Hatzivassiloglou and Kevin Knight},
booktitle = {Proc. 14th Int. Joint Conf. Artificial Intelligence},
publisher = {Morgan-Kaufmann},
address = {2929 Campus Dr., Suite 260, San Mateo, CA, 94403, USA},
pages = {1382--1389},
month = {August},
year = {1995},
url = {http://www.isi.edu/natural-language/mt/ijcai95-glosser.ps},
comment = {Text from section 4.3 of the paper: ``Consequently, a method
is needed to efficiently search the word lattice and select a small set
of highly likely translations. We adopted the $N$-best algorithm for
this purpose [Chow and Schwartz, 1989]. Unlike the widely used Viterbi
algorithm [Viterbi, 1967], which only produces a single best scoring
path, this algorithm offers the advantage of producing any number of
the highest scoring paths in the lattice; these paths can then be rescored
with a more extensive (and expensive) method. It also offers controlled
accuracy (i.e., the extent of suboptimality can be arbitrarily decreased
by the amount of memory made available to the search), and empirical
studies [Nguyen et al., 1994] have shown that it performs equally well
with other, more complicated methods. Finally, no forward estimates of
the viability of a partial path are required (as is, for example, the
case in the $A^\ast$ or stack decoder [Jelinek et al, 1975; Bahl et al.,
1983] algorithm.''}}
@article{Hen-EJOR-86,
title = {{The shortest path problem with two objective functions}},
author = {Mordechai I. Henig},
journal = {Eur. J. Operational Research},
volume = {25},
number = {2},
pages = {281--291},
year = {1986},
review = {MR-87e-90036}}
@article{MR-87e-90036,
reviews = {Hen-EJOR-86},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{The shortest path problem with two objective functions}},
volume = {87e},
number = {90036},
year = {1987},
text = {We present methods to find the shortest path in a network where
each path is associated with two objective. We describe how to obtain
the nondominated paths and the extreme nondominated paths, and compare
the expected complexity of the methods. An improvement in efficiency
can be obtained when quasiconcave or quasiconvex utility functions are
assumed. In the first case, we describe how to find the optimal exteme
nondominated path and bounds for the optimal path value. Then the optimal
path can be located by calculating the $k$th shortest path. In the second
case we suggest a branch and bound method to solve the problem.}}
@inproceedings{HenCraCli-OPTI-98,
title = {{A multiple objective approach to QoS routing in integrated communication
networks}},
author = {Hengeller Antunes, C. and J. M. F. Craveirinha and J. C. N. Cl{\'\i}maco
and C. Barrico},
booktitle = {Proc. Optimization 98},
month = {July},
year = {1998}}
@inproceedings{HerMic-SIT-97,
title = {{Robust estimation of point process intensity features using $k$-minimal
spanning trees}},
author = {A. O. Hero and O. Michel},
booktitle = {Proc. Int. Symp. Information Theory},
publisher = {IEEE},
pages = {74},
month = {June},
year = {1997},
abstract = {Minimal spanning trees (MST) have been applied to multi-dimensional
random processes for pattern recognition and randomness testing. We present
a robust version of the MST to estimate complexity features of a point
process intensity function under an epsilon contaminated model for the
intensity. The principal feature considered is the Renyi entropy of the
mixture and a strongly consistent entropy estimator is given which depends
on the data only through the total length of the MST passing through
the data points. Robustification of the MST estimator is achieved by
applying the theory of k-minimum MST.}}
@article{HigHogWei-EJOR-97,
title = {{Evaluating the demand for supergauge trucks-on-trains services
in Western Europe}},
author = {J. Higginson and T. Hogan and M. Weil},
journal = {Eur. J. Operational Research},
volume = {97},
number = {2},
pages = {293--307},
month = {March},
year = {1997},
abstract = {We investigate the potential diversion of freight traffic from
road to a new rail service in Western Europe. The research aims to predict
broad estimates of the traffic diverting to the rail service using a
network model and algorithms which optimise the use of time and hence
cost for each journey. Traffic diversion is evaluated using a multinomial
logit model which allocates volume across the set of shortest paths relevant
to a given journey. Results from a case study are presented.}}
@article{HisNit-SCJ-95,
title = {{A generalized algorithm for Japanese morphological analysis and
a comparative evaluation of some heuristics}},
author = {T. Hisamitsu and Y. Nitta},
journal = {Systems {\&} Computers in Japan},
volume = {26},
number = {1},
pages = {73--87},
month = {January},
year = {1995},
abstract = {In ordinary written Japanese, words are not separated by spaces.
Therefore morphological analysis involves segmenting and tagging sentences.
Since each sentence has a huge number of possible tagged segmentation,
various criteria have been proposed for making plausible decisions. However,
there are still no unified frameworks that incorporate various heuristics,
and there has been no comparative evaluation of commonly used heuristics.
This paper presents a clear framework to describe various heuristics,
and an $N$-best algorithm for extracting optimal solutions. The time
complexity of this algorithm is $O(nN\log_2(1+N))$, where $n$ is the
sentence length. The advantage of the $N$-best algorithm over the standard
beam search algorithm is also discussed. This paper also presents a comparative
evaluation of three major heuristics, and proposes a precise and portable
rule-based heuristic. Estimation was done using the aforementioned algorithm
and six criteria. The newly proposed heuristic is based upon the Extended
Least Bunsetsu (Phrase) Number method.}}
@inproceedings{Hjo-INFORMS-98,
title = {{A $k$-shortest path column generator for the pairing problem}},
author = {Curt A. Hjorring},
booktitle = {INFORMS/CORS Montr{\'e}al '98},
year = {1998},
abstract = {The rules that define pairings are complex and were previously
hard coded into column generators. A more general solution is a rule
system that returns a simple yes/no for a partial/complete pairing. We
present results from a rule system-based column generator that uses a
k-shortest path algorithm.}}
@article{HofPav-JACM-59,
title = {{A method for the solution of the $N$th best path problem}},
author = {Walter Hoffman and Richard Pavley},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {6},
pages = {506--514},
year = {1959},
annote = {This paper considers the problem of finding the $n$ shortest
paths (allowing loops) between a pair of terminals in a directed network,
with the intended application of analyzing a road network (having distance
equal to vehicular travel time). It is the first published paper on this
subject of which I [DE, 24 July 1998] am aware, but it refers to another
algorithm in an earlier unpublished manuscript by ``Bock, Kantner, and
Haynes of the Armour Research Foundation'' which I have omitted from this
bibliography due to lack of any other detail than those surnames.
The paper defines path $Q$ to be a deviation of a path $P$ if it consists
of a segment of a shortest path tree, followed by a single edge, followed
by a segment of $P$. The authors then prove that the $n$th path is a
deviation of one of the previous paths; their algorithm consists of finding
each successive path by selecting the best among all deviations of all
previously listed paths. The same idea of representing paths as deviations
is central to my own paper ``Finding the $k$ shortest paths'', in which
I unfortunately neglected to cite the present reference.
There is also a brief footnote discussing the problem of finding loopless
paths: ``If it is desired to avoid paths containing loops, $j$ must be
suitably restricted'' where $j$ is the destination of a deviation edge.
This footnote seems incorrect, since there are networks in which the
second-shortest loopless path is not a deviation of the shortest path.
No worst-case analysis is given, although the authors give some heuristic
estimates based on the assumption that the network resembles a square
grid, in which case they estimate the time to be roughly $O(k\sqrt{n})$
(I guess not counting the time to find the initial shortest path tree,
and with $k$ not too big). The authors' implementation is not completely
naive: they construct the deviations of each path only once, and save
memory by only storing the $n$ best deviations found so far. It seems
from their $O(k\sqrt{n})$ estimate that they understood how to compute
each deviation in constant time, but (for pathological networks) each
path can have $\Theta(km)$ deviations, so their worst case should have
been asymptotically $O(k^2m)$. Some computational results of an implementation
on an IBM 650 are also included: for a given 99-node planar network,
their code took 5 minutes to find the shortest path tree and 18 minutes
to find the ten best paths.
No abstract was included in the original paper.},
review = {MR-23-B2056}}
@article{MR-23-B2056,
reviews = {HofPav-JACM-59},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A method for the solution of the $N$th best path problem}},
author = {Edward F. Moore},
volume = {23},
number = {B2056},
year = {1962}}
@inproceedings{HolSve-NORSIG-95,
title = {{Training of lexica for subword-based speech recognisers}},
author = {T. Holter and T. Svendsen},
journal = {Proc. Norwegian Signal Processing Symp.},
publisher = {Hogskolen i Stavanger},
pages = {57--61},
month = {September},
year = {1995},
abstract = {In this paper we present an automatic optimal baseform determination
algorithm. Given a set of subword hidden Markov models (HMMs) and acoustic
tokens of a specific word, we apply the tree-trellis $N$-best search
algorithm to find the optimal baseforms (transcriptions) in the maximum
likelihood sense. The proposed algorithm is used in an iterative manner,
creating a series of lexica trained from the given acoustic tokens. The
DARPA resource management (RM) database was used for evaluating the new
baseform optimisation algorithm. When compared to the initial lexicon
derived from the DARPA RM-distribution, improvements of recognition rates
have been obtained for all lexica trained with the baseform optimisation
algorithm. An analysis of the relative performances of the lexica is
given.}}
@article{Hor-JORS-80,
title = {{Finding the $K$ least cost paths in an acyclic activity network}},
author = {G. J. Horne},
journal = {J. Operational Research Soc.},
volume = {31},
pages = {443--448},
year = {1980},
abstract = {Presents an application of the Kth shortest path problem to
an agricultural problem-dairy waste management. It goes on to compare
several algorithms for this problem and concludes by using computational
results to provide a basis for choosing the most appropriate algorithm
for a variety of applications.}}
@mastersthesis{Hsu-MS-92,
title = {{Load balanced $K$-shortest path routing for circuit-switched
networks}},
author = {Chi-Feng Hsu},
school = {Rutgers Univ., Dept. Electrical {\&} Computer Engineering},
month = {May},
year = {1992}}
@inproceedings{HsuHui-RCC-94,
title = {{Load-balanced $K$-shortest path routing for circuit-switched
networks}},
author = {Chi-Feng Hsu and Joseph Y. Hui},
booktitle = {Proc. IEEE NY/NJ Regional Control Conf.},
month = {August},
year = {1994},
url = {http://www-caip.rutgers.edu/~chifeng/mieee.ps},
abstract = {Issue of the load-balanced $K$-shortest path routing are investigated
in this paper, including multiple alternative routing strategies, network
loss performance, and optimal interval for network status updates. A
max-min cost function for alternative path evaluation is applied to Least
Loaded Routing model in circuit-switched networks. Two kinds of routing
strategy which may update the network status instantaneously or periodically
are proposed. Simulation results are then compared and analyzed.}}
@article{HsuLuc-DM-94,
title = {{On the $k$-diameter of $k$-regular $k$-connected graphs}},
author = {D. Frank Hsu and Tomasz {\L}uczak},
journal = {Discrete Mathematics},
volume = {133},
pages = {291--296},
year = {1994},
review = {MR-95g-05041}}
@article{MR-95g-05041,
reviews = {HsuLuc-DM-94},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On the $k$-diameter of $k$-regular $k$-connected graphs}},
author = {Hans L. Bodlaender},
volume = {95g},
number = {05041},
year = {1995},
text = {The $k$-distance $d\sb k(v,w)$ between two vertices $v,w$ in a
graph $G=(V,E)$ is the length of the $k$-shortest path between $v$ and
$w$. The $k$-diameter of $G$ is the maximum $k$-distance over all pairs
of vertices. Several results are obtained on the maximal value of the
$k$-diameter that can be achieved for $k$-connected graphs with $n$ vertices.
Among other results, the authors show that every $k$-regular $k$-connected
graph on $n$ vertices has $k$-diameter at most $n/2$. This bound is sharp
when $n=4k-6+i(2k-4)$, e.g., when $n$ is even and $k=3$.}}
@article{Hua-JORS-95,
title = {{A combined algorithm for solving and calibrating the stochastic
traffic assignment model}},
author = {Hai-Jun Huang},
journal = {J. Operational Research Soc.},
volume = {46},
pages = {977--987},
year = {1995},
abstract = {This paper studies Fisk's stochastic user equilibrium (SUE)
assignment model in which travellers are assumed not to have perfect
knowledge of the traffic system. It is shown that the stochastic properties
of this model completely depend on the calibration parameter. After giving
the searching method of an 'efficient paths' set, a modified combined
algorithm for solving and calibrating Fisk's stochastic traffic assignment
model is developed. In this algorithm, the path enumeration is achieved
automatically in the preliminary phase and renewed in the iterative processes,
and the number of alternative paths generated can be controlled by a
predetermined function. Two numerical examples are presented to illustrate
the model's properties and the algorithm's efficiencies.}}
@article{HuaMil-AAM-91,
title = {{A time-efficient, linear-space local similarity algorithm}},
author = {Xiaoqiu Huang and Webb Miller},
journal = {Advances in Applied Math.},
volume = {12},
number = {3},
pages = {337--357},
year = {1991},
review = {MR-92f-92025}}
@article{MR-92f-92025,
reviews = {HuaMil-AAM-91},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A time-efficient, linear-space local similarity algorithm}},
volume = {92f},
number = {92025},
year = {1992},
text = {A dynamic programming algorithm to determine similar regions of
two sequences is presented. The method produces $k$ best ``nonintersecting''
local alignments, for any chosen $k$. The procedure is an improvement
of an earlier algorithm of the authors, which while retaining the linear
space characteristic, lowers the time requirement. If $M$ and $N$ are
the lengths of the given sequences and $K$ is the total length of the
computed alignments, the space requirement is $O(M+N+K)$ while ``under
reasonable assumptions'', the running time is $O(MN+\sum_{n=1}^k L_n^2$,
where $L_n$ is the length of the $n$th computed alignment. An example
is given and the results of test runs, comparing the algorithm's performance
with its predecessor on a pair of DNA sequences of $73\,360$ and $44\,954$
nucleotides containing the $\beta$-like globin cluster from humans and
rabbits, are reported.}}
@article{Hur-MR-82a,
title = {{A Petri net approach to enumerate all system success paths for
reliability evaluation of a complex system}},
author = {G. S. Hura},
journal = {Microelectronics and Reliability},
volume = {22},
number = {3},
pages = {427--428},
year = {1982},
abstract = {A Petri net approach to enumerate all system success paths
between a specified pair of nodes is presented. The proposed technique
requires only vector additions on a single matrix. It is simple and can
easily be computerized.}}
@article{Hur-MR-82b,
title = {{Enumeration of success paths in a graph}},
author = {G. S. Hura},
journal = {Microelectronics and Reliability},
volume = {22},
number = {5},
pages = {1033--1034},
year = {1982},
abstract = {A computer program for enumeration of all success paths between
a specified pair of nodes in a probabilistic nonoriented graph is described.
It can easily be adapted for use with oriented graphs.}}
@article{Hur-MR-83,
title = {{Enumeration of all simple paths in a directed graph using Petri
net: a systematic approach}},
author = {G. S. Hura},
journal = {Microelectronics and Reliability},
volume = {23},
number = {1},
pages = {157--159},
year = {1983},
abstract = {The determination of all simple (or success) paths between
two specified nodes in a directed graph finds various applications in
graph theory, reliability evaluation of a system, etc. Many attempts
at the problem of determining the $S$-$T$ paths (simple or success paths
between specified nodes $S$ and $T$) have appeared in the literature.
The author utilizes the concept of the Petri net as yet another attempt
at the same problem. The proposed technique is simple and tackles the
problem in a systematic way and is amenable to computer implementation.}}
@article{IkeMatTam-DAM-93,
title = {{Adjacency of the best and second best valued solutions in combinatorial
optimization problems}},
author = {Y. Ikebe and Tomomi Matsui and A. Tamura},
journal = {Discrete Applied Mathematics},
volume = {47},
number = {3},
pages = {227--232},
year = {1993},
review = {MR-94i-90104}}
@article{MR-94i-90104,
reviews = {IkeMatTam-DAM-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Adjacency of the best and second best valued solutions in combinatorial
optimization problems}},
volume = {94i},
number = {90104},
year = {1994},
text = {We say that a polytope satisfies the strong adjacency property
if every best valued extreme point of the polytope is adjacent to some
second best valued extreme point for any weight vector. Perfect matching
polytopes satisfy this property. In this paper, we give sufficient conditions
for a polytope to satisfy the strong adjacency property. From this, binary
$b$-matching polytopes, set partitioning polytopes, set packing polytopes,
etc. satisfy the strong adjacency property.}}
@article{Ish-JORSJ-78,
title = {{A new method finding the $K$th best path in a graph}},
author = {Hiroaka Ishii},
journal = {J. Oper. Res. Soc. Japan},
volume = {21},
number = {4},
pages = {469--476},
year = {1978},
review = {MR-81a-05078}}
@article{MR-81a-05078,
reviews = {Ish-JORSJ-78},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A new method finding the $K$th best path in a graph}},
author = {Kenji Onaga},
volume = {81a},
number = {05078},
year = {1981},
text = {This paper presents a new algorithm determining the Kth best path
without any circuit between two specified vertices in a connected, simple
and nonoriented graph. The method presented here is based on the well-known
fact that the minimum set of ring sum of several Euler graphs and a special
path between two vertices consists of all paths between the vertices.
Lastly, an illustrative example is given and the efficiency of the algorithm
is estimated approximately.}}
@article{JanZemSki-TCS-92,
title = {{Precise rank-ordering of all paths through an interconnection
network}},
author = {Y.-F. Jan and A. H. Zemanian and Steven S. Skiena},
journal = {Trans. Circuits and Systems},
publisher = {IEEE},
volume = {39},
number = {12},
pages = {1011--1014},
month = {December},
year = {1992},
abstract = {A method for precisely ranking all the input-to-output transmission
paths in an interconnection network is given. It is based upon the superposition
principle along with a novel technique for decomposing the network into
simpler networks, each having exactly one input-to-output path. The output
voltages of the latter networks sum to that of the original network and
determine the ranks. The procedure can be used for both DC and AC steady-state
regimes. It can also ascertain whether an intended transmission path
in a circuit design truly dominates all other paths.}}
@phdthesis{Jay-PhD-92,
title = {{In-Vehicle Information Systems for Network Traffic Control: A
Simulation Framework to Study Alternative Guidance Strategies}},
author = {R. Jayakrishnan},
school = {Univ. of Texas, Austin, Dept. of Civil Engineering},
year = {1992},
abstract = {Efforts are underway around the world to use advanced telecommunication
and information technologies for improving the traffic quality in congested
urban areas through new approaches to effect better traffic patterns.
However these efforts to-date have proceeded without much insights on
several key elements with profound effect on the resulting system performance.
This research develops a simulation framework to study certain aspects
that influence the performance of traffic networks under information.
A framework is developed that integrates the modelling of three key elements
of traffic systems under information, namely, the traffic flow simulation,
the path-processing aspects and the driver response to information. The
simulation moves the vehicles using macroscopic traffic flow relations
in discretized network segments, while tracking their positions. The
boundedly rational behavioral model assumed for the driver response captures
the driver decisions to stay on suboptimal but sufficing paths despite
the provided route information. The framework is applied to candidate
networks under information, to study the system performance under different
levels of usage of technology and different driver behavior parameters.
Two different programs were developed: one for networks with parallel
highways towards a single destination, and one for networks of general
shapes and multiple destinations. The former model with faster path processing
is also used for studying an idealized corridor for its stochastic-dynamic
equilibration behavior under information using iterative simulations
with available utility functions. The latter model is used for a realistic
city network similar to the core network of Austin, Texas. The path processing
component is developed carefully, and is flexible enough to model the
driver behavior of selecting from a few paths under non-mandatory guidance.
Efficient data structures are used for the efficient enumeration and
updating of k-shortest paths. If these paths are not updated every simulation
time step, the trip times on the existing k-paths are updated by efficient
routines using two possible algorithms: one intended for sequential processors
and another for a processor with vectorization capabilities. The results
provide important insights on the effectiveness of in-vehicle information.
Only a relatively small fraction (less than 30{\%}) of the drivers may need
to be equipped to obtain almost all of the advantages of guidance, and
the system could get worse for higher percentages depending on the network
context.}}
@inproceedings{JayThu-CGT-80,
title = {{Analysis of a spanning tree enumeration algorithm}},
author = {Rajagopalan Jayakumar and K. Thulasiraman},
booktitle = {Combinatorics and Graph Theory},
number = {885},
series = {Lecture Notes in Mathematics},
publisher = {Springer Verlag},
pages = {284--289},
year = {1980},
review = {MR-83f-68072}}
@article{MR-83f-68072,
reviews = {JayThu-CGT-80},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Analysis of a spanning tree enumeration algorithm}},
volume = {83f},
number = {68072},
year = {1983},
text = {Enumeration of all the spanning trees of a graph is one of the
widely studied graph problems. Several methods have been proposed for
listing all the spanning trees of a graph. Minty's method and Gabow and
Meyer's method are known to be very efficient. In 1968 J. P. Char [IEEE
Trans. Circuit Theory 15 (1968), 228 - 238; MR 39 {\#}6779] presented a
conceptually simple and elegant algorithm. In this paper we present an
analysis of Char's algorithm and report some interesting behaviour of
this algorithm.}}
@article{JayThuSwa-TCS-84,
title = {{Complexity of computation of a spanning tree enumeration algorithm}},
author = {Rajagopalan Jayakumar and K. Thulasiraman and M. N. Swamy},
journal = {Trans. Circuits and Systems},
publisher = {IEEE},
volume = {31},
number = {10},
pages = {853--860},
year = {1984},
review = {MR-86g-68074}}
@article{MR-86g-68074,
reviews = {JayThuSwa-TCS-84},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Complexity of computation of a spanning tree enumeration algorithm}},
volume = {86g},
number = {68074},
year = {1986},
text = {In 1968, J. P. Char [IEEE Trans. Circuit Theory 15 (1968), 228--238;
MR 39 {\#}6779] presented an algorithm to enumerate all the spanning trees
of an undirected graph $G$. This algorithm starts with a known initial
spanning tree of $G$, and generates all the other spanning trees along
with certain spanning nontree subgraphs of $G$. In this paper a detailed
complexity analysis of Char's algorithm and methods to speed up the algorithm
are discussed. Two heuristics for the selection of the initial spanning
tree are suggested. These heuristics result in a considerable reduction
in the number of spanning nontree subgraphs generated. A technique called
path compression, aimed at reducing the actual number of comparisons,
is described. Computational results on several randomly generated graphs
are presented to illustrate the improvement achieved.}}
@article{JayThuSwa-TCS-89,
title = {{MOD-CHAR: an implementation of Char's spanning tree enumeration
algorithm and its complexity analysis}},
author = {Rajagopalan Jayakumar and K. Thulasiraman and M. N. Swamy},
journal = {Trans. Circuits and Systems},
publisher = {IEEE},
volume = {36},
number = {2},
pages = {219--228},
year = {1989},
review = {MR-90h-68060}}
@article{MR-90h-68060,
reviews = {JayThuSwa-TCS-89},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{MOD-CHAR: an implementation of Char's spanning tree enumeration
algorithm and its complexity analysis}},
volume = {90h},
number = {68060},
year = {1990},
text = {An implementation, called MOD-CHAR, of J. P. Char's spanning tree
enumeration algorithm [same journal 15 (1968), 228--238; MR 39 {\#}6779]
is discussed. Two complexity analyses of MOD-CHAR are presented. It is
shown that MOD-CHAR leads to better complexity results for Char's algorithm
than those obtained using the straightforward implementation implied
in Char's original presentation. The class of graphs for which MOD-CHAR
and, hence, Char's algorithm has linear time complexity per spanning
tree generated is identified. Using a result due to Matula on random
graphs, it is proved that for almost all graphs MOD-CHAR has linear worst-case
time complexity per spanning tree generated. It is also shown that for
any complete graph MOD-CHAR requires, on the average, at most seven computational
steps to generate a spanning tree. This result and computational experiences
provide evidence to believe that for dense graphs of any order the time
complexity of MOD-CHAR is $O(t)$, where $t$ is the number of spanning
trees generated. On the other hand, there is enough evidence to conclude
that for sparse graphs, Char's original implementation is superior to
MOD-CHAR.}}
@inproceedings{JimMar-APR-00,
title = {{Computation of the $N$ best parse trees for weighted and stochastic
context-free grammars}},
author = {Jim{\'e}nez Pelayo, V{\'\i}ctor Manuel and Marzal Var{\'o}, Andr{\'e}s},
booktitle = {Advances in Pattern Recognition: Proc. Joint IAPR 8th Int.
Worksh. Structural and Syntactic Pattern Recognition and 3rd Int. Worksh.
Statistical Pattern Recognition},
number = {1876},
editor = {F. J. Ferri and J. M. I{\~n}esta and A. Amin and P. Pudil},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {183--192},
year = {2000},
url = {http://terra.act.uji.es/~vjimenez/sspr2000.ps.gz},
abstract = {Context-Free Grammars are the object of increasing interest
in the pattern recognition research community in an attempt to overcome
the limited modeling capabilities of the simpler regular grammars, and
have application in a variety of fields such as language modeling, speech
recognition, optical character recognition, computational biology, etc.
This paper proposes an efficient algorithm to solve one of the problems
associated to the use of weighted and stochastic Context-Free Grammars:
the problem of computing the N best parse trees of a given string. After
the best parse tree has been computed using the CYK algorithm, a large
number of alternative parse trees are obtained, in order by weight (or
probability), in a small fraction of the time required by the CYK algorithm
to find the best parse tree. This is confirmed by experimental results
using grammars from two different domains: a chromosome grammar, and
a grammar modeling natural language sentences from the Wall Street Journal
corpus.}}
@article{JimMar-APRA-94,
title = {{A new algorithm for finding the $N$ best sentence hypotheses
in continuous speech recognition}},
author = {Jim{\'e}nez Pelayo, V{\'\i}ctor Manuel and Marzal Var{\'o}, Andr{\'e}s},
journal = {Advances in Pattern Recognition and Applications},
note = {To appear}}
@inproceedings{JimMar-WAE-99,
title = {{Computing the $K$ shortest paths: a new algorithm and an experimental
comparison}},
author = {Jim{\'e}nez Pelayo, V{\'\i}ctor Manuel and Marzal Var{\'o}, Andr{\'e}s},
booktitle = {Proc. 3rd Worksh. Algorithm Engineering},
month = {July},
year = {1999},
url = {http://terra.act.uji.es/REA/papers/wae99.ps.gz},
abstract = {A new algorithm to compute the K shortest paths (in order of
increasing length) between a given pair of nodes in a digraph with n
nodes and m arcs is presented. The algorithm recursively and efficiently
solves a set of equations which generalize the Bellman equations for
the (single) shortest path problem and allows a straightforward implementation.
After the shortest path from the initial node to every other node has
been computed, the algorithm finds the K shortest paths in O(m + K n
log(m/n)) time. Experimental results presented in this paper show that
the algorithm outperforms in practice the algorithms by Eppstein and
by Martins and Santos for different kinds of random generated graphs.}}
@inproceedings{JimMarVid-ES-93,
title = {{Efficient enumeration of sentence hypotheses in connected word
recognition}},
author = {Jim{\'e}nez Pelayo, V{\'\i}ctor Manuel and Marzal Var{\'o}, Andr{\'e}s and E.
Vidal},
booktitle = {Proc. Eurospeech},
pages = {2183--2186},
year = {1993}}
@inproceedings{JinCha-ISCS-89,
title = {{An electrical method for finding suboptimal routes}},
author = {L.-M. Jin and S.-P. Chan},
booktitle = {Int. Symp. Circuits and Systems},
publisher = {IEEE},
volume = {2},
pages = {935--938},
year = {1989},
abstract = {An algorithm is presented for finding the suboptimal routes,
or the kth shortest paths, between two nodes in a network. The algorithm
works by building up an electric computational analogy that consists
of an ideal diode in series with a DC voltage source. The computational
operations increase linearly with the order of k. The algorithm also
works efficiently for finding all routes between two nodes for a given
network.}}
@article{Joh-MST-82,
title = {{A priority queue in which initialization and queue operations
take $O(\log\log D)$ time}},
author = {Donald B. Johnson},
journal = {Mathematical Systems Theory},
volume = {15},
pages = {295--309},
year = {1982}}
@article{JohKas-JACM-78,
title = {{Lower bounds for selection in $X+Y$ and other multisets}},
author = {Donald B. Johnson and Samuel D. Kashdan},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {25},
number = {4},
pages = {556--570},
year = {1978},
review = {MR-80b-68054}}
@article{MR-80b-68054,
reviews = {JohKas-JACM-78},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Lower bounds for selection in $X+Y$ and other multisets}},
author = {Claus-Peter Schnorr},
volume = {80b},
number = {68054},
year = {1980},
text = {It is known that the structure in the multiset $X+Y$, for $X$ and
$Y$ multisets of $n$ real numbers, enables selection to be performed
more quickly than in other sets of size $O(n^2)$. In this paper, a lower
bound of $\Omega(\max(n, K^{1/2}\log K))$ is given for selecting the
$K$th element in $X+X$, and thus in $X+Y$, for $K$ selecting the first
through the median element. Selection of gaps, that is, consecutive differences
in a sorted order, is shown to be $\Omega(n\log n)$ for all $K$. These
results hold also when inputs are restricted to integers. The problem
of selection on $X+X$ can be generalized to selection on the set of multisets
of size m chosen from $X$, where the multisets are ranked on the sums
of their elements. When m and n grow, selection of the $K$th largest
multiset of size $m$ is NP-hard when inputs are expressed in binary notation.
If subsets of $X$ are characterized as paths, circuits or spanning trees
of an edge-weighted graph, then selection of the $K$th largest such subset
of $X$ remains NP-hard. It is not possible to show these problems to
be NP-hard when inputs are expressed in unary, since algorithms exist
which run in time polynomial in the sums of the values of the inputs.}}
@techreport{JohKas-TR-76,
title = {{Lower bounds for selection in $X+Y$ and other multisets}},
author = {Donald B. Johnson and Samuel D. Kashdan},
institution = {Pennsylvania State Univ., Computer Science Dept.},
number = {183},
year = {1976}}
@article{JohMiz-SJC-78,
title = {{Selecting the $K$th element in $X+Y$ and $X_1+X_2+\cdots+X_n$}},
author = {Donald B. Johnson and Tetsuo Mizoguchi},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {7},
number = {2},
pages = {147--153},
year = {1978}}
@inproceedings{JooKimKo-ICSS-94,
title = {{Algorithms for efficient bandwidth utilization on survivable
telecommunication networks}},
author = {U. G. Joo and J. G. Kim and J. S. Ko},
booktitle = {ICCS, Singapore},
publisher = {IEEE},
volume = {3},
pages = {1154--1157},
year = {1994},
abstract = {This paper suggests a line restoration (rerouting) algorithm
based on the minimum cost path (rather than the k-shortest path) for
protection possible link failures and also develops a spare capacity
determination algorithm based on the k-shortest path for the restoration
algorithm. The restoration algorithm can supplement telecommunication
networks with dedicated facility restoration mechanisms, where some intelligent
transmission devices such as broadband digital cross-connect systems
(BDCSs) are involved. These algorithms, described by illustrative examples,
can be utilized in a general network for efficient bandwidth utilization.}}
@inproceedings{JosPilRat-INFORMS-96,
title = {{Variance reduction strategies in route guidance}},
author = {Shirish Joshi and Rekha S. Pillai and Ajay K. Rathi and Suvrajeet
Sen and Jeffrey David Tew},
booktitle = {Proc. Conf. Inst. for Operations Research and the Management
Sciences, Washington},
month = {May},
year = {1996},
abstract = {We illustrate the use of 2 correlation induction strategies
in reducing the variance of travel time estimates in route guidance systems.
Antithetic and control variates are used in a dynamic stochastic k-shortest
path algorithm to reduce the estimate of the mean travel time. This is
motivated by the fact that a route with lower travel time variance is
preferred by some travelers.}}
@inproceedings{JunValFoh-ASSP-95,
title = {{An $N$-best strategy, dynamic grammars and selectively trained
neural networks for real-time recognition of continuously spelled names
over the telephone}},
author = {Jean-Claude Junqua and S. Valente and D. Fohr and J.-F. Mari},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {852--855},
month = {May},
year = {1995},
abstract = {We introduce SmarTspelL, a new speaker-independent algorithm
to recognize continuously spelled names over the telephone. Our method
is based on an $N$-best multi-pass recognition strategy applying costly
constraints when the number of possible candidates is low. This strategy
outperforms an HMM recognizer using a grammar containing all the possible
names. It is also more suitable to real-time implementation. For a 3388
name dictionary, a 95.3{\%} name recognition rate is obtained. A real-time
prototype has been implemented on a workstation. We also present comparisons
of different feature sets for speech representation, and two speech recognition
approaches based on first- and second-order HMMs.}}
@article{Kan-Comb-87,
title = {{Maximum and $k$th maximal spanning trees of a weighted graph}},
author = {Mikio Kano},
journal = {Combinatorica},
volume = {7},
number = {2},
pages = {205--214},
year = {1987},
review = {MR-88k-05064}}
@article{MR-88k-05064,
reviews = {Kan-Comb-87},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Maximum and $k$th maximal spanning trees of a weighted graph}},
author = {R. E. Pippert},
volume = {88k},
number = {05064},
year = {1988},
text = {Let $G$ be a weighted graph. A spanning tree $A$ of $G$ having
maximum weight is called a maximum spanning tree. Let $P$ be any other
spanning tree of $G$. The author shows the existence of a bijection $\Psi\colon
A\sbs P\to P\sbs A$ such that, for every edge $a\in A\sbs P$, $Q\equiv(P\sbs\Psi(a))\cup
a$ is a spanning tree of $G$ with weight at least as large as that of
$P$. This result is used to address interpolation-type problems for spanning
trees of weighted graphs. Several earlier results are given with shorter
proofs, and additional results are also established.}}
@article{KapRam-SJC-95,
title = {{Algorithms for enumerating all spanning-trees of undirected and
weighted graphs}},
author = {Sanjiv Kapoor and H. Ramesh},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {24},
number = {2},
pages = {247--265},
month = {April},
year = {1995},
note = {In this paper, we present algorithms for enumeration of spanning
trees in undirected graphs, with and without weights. The algorithms
use a search tree technique to construct a computation tree. The computation
tree can be used to output all spanning trees by outputting only relative
changes between spanning trees rather than the entire spanning trees
themselves. Both the construction of the computation tree and the listing
of the trees is shown to require O(N + V + E) operations for the case
of undirected graphs without weights. The basic algorithm is based on
swapping edges in a fundamental cycle. For the case of weighted graphs
(undirected), we show that the nodes of the computation tree of spanning
trees can be sorted in increasing order of weight, in O(N log V + VE)
time. The spanning trees themselves can be listed in O(NV) time. Here
N, V, and E refer, respectively, to the number of spanning trees, vertices,
and edges of the graph.}}
@inproceedings{KapRam-WADS-91,
title = {{Algorithms for enumerating all spanning-trees of undirected and
weighted graphs}},
author = {Sanjiv Kapoor and H. Ramesh},
booktitle = {Proc. 2nd Worksh. Algorithms {\&} Data Structures},
number = {519},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {461--472},
year = {1991}}
@inproceedings{KarAya-BON-96,
title = {{Effects of wavelength routing and selection algorithms on wavelength
conversion gain in WDM}},
author = {E. Karasan and E. Ayanoglu},
booktitle = {Proc. Conf. Broadband Optical Networks},
publisher = {IEEE},
month = {August},
year = {1996},
abstract = {We propose two $k$ shortest path algorithms for selecting the
route-wavelength pair in WDM networks with and without wavelength converters
with orders of magnitude larger conversion gains as compared to conventional
routing. We state a conclusion on the use of wavelength converters in
long-distance networks.}}
@article{KatIbaMin-ECJ-78,
title = {{An $O(Kn^2)$ algorithm for $K$ shortest simple paths in an undirected
graph with nonnegative arc length}},
author = {Naoki Katoh and Toshihide Ibaraki and Hisashi Mine},
journal = {Electronics and Communications in Japan},
volume = {61},
number = {12},
pages = {1--8},
year = {1978},
review = {MR-83g-68044}}
@article{MR-83g-68044,
reviews = {KatIbaMin-ECJ-78},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An $O(Kn^2)$ algorithm for $K$ shortest simple paths in an undirected
graph with nonnegative arc length}},
volume = {83g},
number = {68044},
year = {1983},
text = {We present an O(Kn{sup}2) algorithm to find K shortest simple paths
in an undirected graph with nonnegative arc length. Here n is the number
of vertices in the graph. First a shortest simple path is obtained by
the Dijkstra method. The second through kth shortest simple paths are
then successively obtained by systematically partitioning the set of
paths to avoid duplication. The partitioning is accomplished by repeatedly
calling a subroutine to find in O(n{sup}2) time the shortest simple paths
not containing a given initial subpath of the first shortest simple path.
The present algorithm seems to be better than any other existing algorithm
for K shortest simple paths.}}
@article{KatIbaMin-IECE-78,
title = {{An $O(Kn^2)$ algorithm for $K$ shortest simple paths in an undirected
graph with nonnegative arc length}},
author = {Naoki Katoh and Toshihide Ibaraki and Hisashi Mine},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E61},
pages = {971--972},
year = {1978},
abstract = {This paper presents an algorithm for finding the $k$-th shortest
simple paths $P^k$ for $k=1, 2,\ldots,K$ from node $s$ in $V$ to node
$t$ in $V$. The subroutine obtains in $O(n^2)$ time the shortest simple
path under the additional constraint that it branches from a specified
initial portion of the first shortest path.}}
@article{KatIbaMin-JACM-81,
title = {{An algorithm for the $K$ best solutions of the resource allocation
problem}},
author = {Naoki Katoh and Toshihide Ibaraki and Hisashi Mine},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {28},
number = {4},
pages = {752--764},
year = {1981},
review = {MR-83m-90048}}
@article{MR-83m-90048,
reviews = {KatIbaMin-JACM-81},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An algorithm for the $K$ best solutions of the resource allocation
problem}},
author = {Jan Karel Lenstra},
volume = {83m},
number = {90048},
year = {1983},
text = {The resource allocation problem considered here is the problem
of minimizing $\sum_{i=1}^n f_i(x_i)$ subject to $\sum_{i=1}^n x_i=N$
and $x_i\in N$, where the $f_i$ are convex functions over $[0, N]$ and
$n\in N$. This problem is solvable in low-order polynomial time; for
the most efficient approach, see work of G. N. Frederickson and D. B.
Johnson [``Optimal algorithms for generating quantile information in $X+Y$
and matrices with sorted columns'', TR CS-79-45, Pennsylvania State Univ.,
College Park, Pa., 1979; per bibl.]. The authors develop an algorithm
for obtaining the $K$ best solutions to this problem, which requires
$O(T^\ast+K\log{K}+K\sqrt{n\log{n}})$ time and $O(K\sqrt{n\log{n}}+n)$
space, where $T^\ast$ is the time required to find the optimal solution.
The algorithm is based on the framework given by E. L. Lawler [Management
Sci. 18 (1972), 401 - 405; MR 45 {\#}1575].}}
@article{KatIbaMin-Nw-82,
title = {{An efficient algorithm for $K$ shortest simple paths}},
author = {Naoki Katoh and Toshihide Ibaraki and Hisashi Mine},
journal = {Networks},
volume = {12},
number = {4},
pages = {411--427},
year = {1982},
review = {MR-84i-90059}}
@article{MR-84i-90059,
reviews = {KatIbaMin-Nw-82},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An efficient algorithm for $K$ shortest simple paths}},
author = {M. M. Sys{\l}o},
volume = {84i},
number = {90059},
year = {1984},
text = {This paper presents an algorithm for obtaining $K$ shortest paths
(i.e., paths contain no cycles) between two specified nodes in an undirected
graph with nonnegative edge lengths. Its running time is $O(K\cdot c(n,
m))$, where $n$ is the number of nodes, $m$ is the number of edges in
a graph, and $c(n,m)$ is the time to compute shortest paths from one
node to all the other nodes. The time bound of the proposed algorithm
is better than those of other algorithms, the best of which (proposed
by Yen) requires $O(Kn^3)$ time and $c(n,m)\le\min(O(n^2),O(m\log n))$.}}
@article{KatIbaMin-SJC-81,
title = {{An algorithm for finding $k$ minimum spanning trees}},
author = {Naoki Katoh and Toshihide Ibaraki and Hisashi Mine},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {10},
number = {2},
pages = {247--255},
year = {1981},
review = {MR-82k-68037}}
@article{MR-82k-68037,
reviews = {KatIbaMin-SJC-81},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An algorithm for finding $k$ minimum spanning trees}},
volume = {82k},
number = {68037},
year = {1982},
text = {We present an algorithm for finding $K$ minimum spanning trees
in an undirected graph. The required time is $O(Km+\min(n^2, m\log\log
n))$ and the space is $O(K+m)$, where $n$ is the number of vertices and
$m$ is the number of edges. The algorithm is based on three subroutines.
The first two subroutines are used to obtain the second minimum spanning
tree on $O(\min(n^2, m\alpha (m, n)))$ steps, where $\alpha (m, n)$ is
Tarjan's inverse of Ackermann's function [M. Blum et al., J. Comput.
System Sci. 7 (1973), 448 - 461; MR 48 {\#}8256] which is very slowly growing.
The third one obtains the kth minimum spanning tree in $O(m)$ steps when
the $j$th minimum spanning trees for $j=1,2,\ldots,k-1$ are given.}}
@inproceedings{KatTra-ACSC-95,
title = {{Simple parallel algorithms for the replacement edge problem and
related problems on spanning trees}},
author = {Jyrki Katajainen and J. L. Traff},
booktitle = {Proc. 18th Australasian Computer Science Conf.},
number = {1},
series = {Australian Computer Science Communications},
volume = {17},
pages = {254--261},
month = {February},
year = {1995},
abstract = {Let $G$ ($G'$) be a connected, undirected (directed), weighted
graph with $n$ vertices and $m$ edges. Further, let $S$ be a spanning
tree of $G$, $T$ a minimum spanning tree of $G$, and $U$ a shortest path
tree of $G'$. In this paper simple parallel algorithms are presented
for the following problems: (a) Finding replacement edge for minimum
spanning tree edges: Given $G$ and $T$, determine, for each edge $e$
of $T$, a non-tree edge $f$ by which $e$ should be replaced to create
a new minimum spanning tree if $e$ is removed from $G$. (b) Finding the
most vital edge with respect to minimum spanning trees: Given $G$, determine
a most vital edge of $G$ (with respect to minimum spanning trees), that
is, an edge whose removal from $G$ has the largest impact on the weight
of a minimum spanning tree of $G$. (c) Verification of minimum spanning
trees: Given $G$ and $S$, determine whether $S$ is a minimum spanning
tree of $G$. (d) Sensitivity analysis for minimum spanning trees: Given
$G$ and $T$, compute, for each edge $e$ of $G$, by how much the weight
of $e$ can change without affecting the minimality of $T$. (e) Sensitivity
analysis for shortest path trees: Given $G'$ and $U$, compute, for each
edge $e$ of $G'$, by how much the weight of $e$ can change without affecting
the minimality of $U$. The algorithms run in $O(\log n)$ time and $O(m)$
space with $m$ processors. The problems (a), (b), (d), and (e) are solved
on a MINIMUM CRCW PRAM, whereas the problem (c) is solved on a CREW PRAM.
The algorithms utilize a simple technique for computing functions defined
on paths in trees that might be of independent interest.}}
@inproceedings{KazSri-PDC-93,
title = {{Fast distributed algorithms for disjoint paths and connectivity}},
author = {A. Kazmierczak and R. Sridhar},
booktitle = {Proc. 6th Int. Conf. Parallel and Distributed Computing},
publisher = {ISCA},
pages = {236--241},
year = {1993},
abstract = {Efficient distributed algorithms for determining vertex disjoint
s-t paths, edge disjoint s-t paths, and testing k-vertex connectivity
in networks is presented in this paper. The vertex (respectively, edge)
disjoint s-t paths problem is defined as follows. Given a graph G with
n vertices and m edges, and two specified vertices s and t, find k vertex
(respectively, edge) disjoint paths between s and t, if they exist.}}
@article{KhaSin-EL-80,
title = {{Petri net approach to enumerate all simple paths in a graph}},
author = {A. A. Khan and H. Singh},
journal = {Electronics Letters},
volume = {16},
number = {8},
pages = {291--292},
month = {April},
year = {1980},
abstract = {A technique utilising the concept of reachability in a Petri
net is proposed to enumerate all simple paths between two specified nodes
of a graph. It is simple and requires little computation.}}
@inproceedings{Khe-HICSS-72,
title = {{A new approach to finding all routes and loops in networks}},
author = {N. A. Kheir},
booktitle = {Proc. 5th Hawaii Int. Conf. System Science},
publisher = {Western Periodicals Co.},
editor = {A. Lew},
pages = {522--524},
month = {January},
year = {1972},
abstract = {THe problem of finding all the routes (paths) between any two
points (nodes) and/or all the loops is of special interest in many of
the areas where systems are represented by networks. In this paper, the
applicability of Mason's Signal Flow Graph, originally developed for
the analysis of complex feedback systems, is extended for non-electrical
engineering problems. An algorithm has been developed based on what is
defined as the `Lines` of the graph. A number of applications are discussed.}}
@article{KimKim-Omega-99,
title = {{A decomposition approach to a multi-period vehicle scheduling
problem}},
author = {Jung-Ug Kim and Yeong-Dae Kim},
journal = {Omega},
volume = {27},
number = {4},
pages = {421--430},
month = {August},
year = {1999},
abstract = {We consider a multi-period vehicle scheduling problem (MPVSP)
in a transportation system where a fleet of homogeneous vehicles delivers
products of a single type from a central depot to multiple (N) retailers.
The objective of the MPVSP is to minimize transportation costs for product
delivery and inventory holding costs at retailers over the planning horizon.
A two-phase heuristic algorithm is suggested based on a k-shortest path
algorithm. In the first phase of the algorithm, the MPVSP is decomposed
into N single-retailer problems by ignoring the number of vehicles available.
In the second phase, a set of vehicle schedules is selected from those
generated in the first phase. The vehicle schedule selection problem
is a generalized assignment problem and it is solved by a heuristic based
on the k-shortest path algorithm. Computational experiments on randomly
generated test problems show that the suggested algorithm gave near optimal
solutions in a reasonable amount of computation time.}}
@inproceedings{KleRaoRau-STOC-94,
title = {{Faster shortest-path algorithms for planar graphs}},
author = {Philip N. Klein and Satish Rao and Monika H. Rauch and Sairam
Subramanian},
booktitle = {Proc. 26th Symp. Theory of Computing},
publisher = {ACM},
pages = {27--37},
year = {1994},
abstract = {We give a linear-time algorithm for single-source shortest
paths in planar graphs with nonnegative edge-lengths. Our algorithm also
yields a linear-time algorithm for maximum flow in a planar graph with
the source and sink on the same face. The previous best algorithms for
these problems required Omega (n square root (log n)) time where n is
the number of nodes in the input graph. For the case where negative edge-lengths
are allowed, we give an algorithm requiring O(n/sup 4/3/ log nL) time,
where L is the absolute valve of the most negative length. Previous algorithms
for shortest paths with negative edge-lengths required Omega (n/sup 3/2/)
time. Our shortest-path algorithm yields an O(n/sup 4/3/ log n)-time
algorithm for finding a perfect matching in a planar bipartite graph.
A similar improvement is obtained for maximum flow in a directed planar
graph.}}
@inproceedings{KniHat-ACL-95,
title = {{Two-level, many-paths generation}},
author = {Kevin Knight and Vasileios Hatzivassiloglou},
booktitle = {Proc. Conf. Assoc. for Computational Linguistics},
pages = {252--260},
year = {1995},
url = {http://www.isi.edu/natural-language/mt/acl95.ps},
comment = {Text from section 7 of the paper: ``Instead of explicitly constructing
all possible renditions of a semantic input $\ldots$ we use a more efficient
data structure and control algorithm to express possible ambiguities.
The data structure is a word lattice---an acyclic state transition network
with one start state, one final state, and transitions labeled by words.
$\ldots$ Once the semantic input to the generator has been transformed
to a word lattice, a search component identifies the $N$ highest scoring
paths from the start to the final state, according to our statistical
language model. We use a version of the $N$-best algorithm (Chow and
Schwartz, 1989), a Viterbi-style beam search algorithm that allows extraction
of more than just the best scoring path. (Hatzivassiloglou and Knight,
1995) has more details on our search algorithm and the method we applied
to estimate the parameters of the statistical model.''}}
@article{KonGreMou-JTE-96,
title = {{Strategy for solving static multiple-optimal path transit network
problems}},
author = {N. Koncz and J. Greenfeld and K. Mouskos},
journal = {J. Transportation Engineering},
publisher = {ASCE},
volume = {122},
number = {3},
pages = {218--225},
year = {1996},
abstract = {The trip making process using transit versus private automobile
differs in the use of time schedules, walking paths, transfer stops,
plus issues such as fare and safety. Due to these factors, many of the
standard shortest path algorithms do not apply. The purpose of this
study is to develop an algorithm and strategy for transit providers to
find best alternatives for the user, and to demonstrate how a geographic
information system can be used in the development of transit advanced
traveler information system (TATIS) to meet these needs. This paper
presents a short introduction to TATIS systems, some commonly used algorithms
in determining the shortest and multiple paths, and anew strategy that
was developed in this study which differs from standard network algorithms.
The major features of this proposed algorithm are: (1) Capability of
handling multiple modes of transit; (2) providing paths that include
walking distances from and to the transit path as well as between transfer
points; and (3) provision of multiple optimal paths to allow the user
flexibility in choosing a path.}}
@article{KonMan-MR-88,
title = {{An improved method of enumerating all trees and minimal paths
in a graph using Petri nets}},
author = {J. M. Kontoleon and D. Mandaltsis},
journal = {Microelectronics and Reliability},
volume = {28},
number = {5},
pages = {783--791},
year = {1988},
abstract = {Two algorithms are presented. The first enumerates all the
trees in a graph while the second enumerates all the minimal paths between
two vertices of a graph. Both algorithms are based on the concept of
reachability in Petri nets and they are fast and simple. These algorithms
always enumerate only real trees and minimal paths while similar earlier
techniques sometimes fail at this point.}}
@article{KubXuXie-GA-97,
title = {{A minimax method for finding the k best ''differentiated'' paths}},
author = {M. Kuby and Z. Y. Xu and X. D. Xie},
journal = {Geographical Analysis},
volume = {29},
number = {4},
pages = {298--313},
month = {October},
year = {1997},
note = {In real-world applications, the k-shortest-paths between a pair
of nodes on a network will often be slight variations of one another.
This could be a problem for many path-based models, particularly those
on a capacitated networks where different routing alternatives are needed
that are less likely to encounter the same capacity constraints. This
paper develops a method to solve for k differentiated paths that are
relatively short and yet relatively different from one another, but not
necessarily disjoint. Our method utilizes the sum of a path's distance
plus some fraction of its shared distance with each other path. A minimax
algorithm is used to select the path whose largest sum of length, plus
shared length vis-a-vis each previously selected path, is as simple as
possible. We present computational results for the Chinese railway system,
comparing the paths generated by a standard k-shortest-path algorithm
with those from our new model.}}
@inproceedings{KuhNieSch-ASSP-94,
title = {{Ergodic hidden Markov models and polygrams for language modeling}},
author = {T. Kuhn and H. Niemann and E. G. Schukat-Talamazzini},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {I/357--360},
month = {April},
year = {1994},
abstract = {Presents two new techniques for language modeling in speech
recognition. The first technique is based on ergodic discrete density
hidden Markov models (HMM) which can be applied to bigrams based on word
categories. This statistical approach of the so-called Markov bigrams
enables an efficient unsupervised learning procedure for the bigram probabilities
with the well-known Baum-Welch algorithm. Furthermore, maximizing the
model-conditional probability is equivalent to minimizing the perplexity
of the training corpus. The second technique is based on polygrams which
are an extension of the bigram ($n=2$) or trigram ($n=3$) grammars to
any possible value of $n$. According to the smoothing techniques for
bigram or trigram models, the probabilities of the $n$-grams in the polygram
model are interpolated using the relative frequencies of all $n'$-grams
with $n'\le n$. Both techniques were evaluated on the ATIS corpus by
computing the test set perplexity. Furthermore the authors integrated
the Markov bigrams as well as the polygrams into their word recognizer
for continuous speech. Experimental results on a German database are
discussed using the $N$-best paradigm to reorder the generated word sequences
according to the sentence probability of the language model.}}
@article{KumGho-CSI-94,
title = {{Parallel algorithm for finding first $K$ shortest paths}},
author = {N. Kumar and R. K. Ghosh},
journal = {Computer Science and Informatics},
volume = {24},
number = {3},
pages = {21--28},
month = {September},
year = {1994}}
@article{Kun-Int-94,
title = {{An incremental algorithm for identification of longest (shortest)
paths}},
author = {S. Kundu},
journal = {Integration, The VLSI Journal},
volume = {17},
pages = {25--31},
year = {1994},
abstract = {In this paper we describe an algorithm that finds the next
k longest or shortest paths of a directed acyclic graph on demand, without
computing all previous paths again. We also suggest a technique to find
longest (shortest) paths through a specific input or a specific output
or a specific input output pair. This algorithm has many applications
including but not limited to timing analysis of digital integrated circuits,
timing driven placement of digital circuits, and delay analysis/routing
of messages in computer communication networks.}}
@article{KwoChaHal-TIE-96,
title = {{Genetic algorithm for optimizing the nonlinear time alignment
of automatic speech recognition systems}},
author = {S. Kwong and C. W. Chau and W. A. Halang},
journal = {Trans. Industrial Electronics},
publisher = {IEEE},
volume = {43},
number = {5},
pages = {559--566},
month = {October},
year = {1996},
abstract = {Dynamic time warping (DTW) is a nonlinear time-alignment technique
for automatic speech recognition (ASR) systems. It had been widely used
in many commercial and industrial products, ranging from electronic dailies/dictionaries
to wireless voice digit dialers. DTW has the advantages of fast training
and searching times, which makes it more popular than other available
ASR techniques. However, there exist some limitations to DTW, such as
the stringent rule on slope weighting, the nontrivial computation of
the K-best paths, and the significant increase in computational time
when the endpoint constraint is relaxed or the variations of the length
of pattern increased. In this paper, a stochastic method called the genetic
algorithm (GA), which is used to solve the nonlinear time alignment problem,
is presented. Experimental results show that the GA has a better performance
than the DTW. In addition two derivatives of GA: the hybrid GA and the
parallel GA are also presented.}}
@article{KwoHeMan-IJPRAI-98,
title = {{Parallel genetic-based hybrid pattern matching algorithm for
isolated word recognition}},
author = {S. Kwong and Q. H. He and K. F. Man and K. S. Tang and C. W.
Chau},
journal = {Int. J. Pattern Recognition {\&} Artificial Intelligence},
volume = {12},
number = {5},
pages = {573--594},
month = {August},
year = {1998},
abstract = {Dynamic time warping (DTW) is a common technique widely used
for nonlinear time normalization of different utterances in many speech
recognition systems. Two major problems are usually encountered when
the DTW is applied for recognizing speech utterances: (i) the normalization
factors used in a warping path; and (ii) finding the K-best warping paths.
Although DTW is modified to compute multiple warping paths by using the
tree-trellis search (TTS) algorithm, the use of actual normalization
factor still remains a major problem for the DTW. In this paper, a parallel
genetic time warping (PGTW) is proposed to solve the above said problems.
A database extracted from the TIMIT speech database of 95 isolated words
is set up for evaluating the performance of the PGTW. In the database,
each of the first 15 words had 70 different utterances, and the remaining
80 words had only one utterance. For each of the 15 words, one utterance
is arbitrarily selected as the test template for recognition. Distance
measure for each test template to the utterances of the same word and
to those of the 80 words is calculated with three different time warping
algorithms: TTS, PGTW and sequential genetic time warping (SGTW). A normal
distribution model is used to evaluate the performance of the three algorithms
analytically. The analyzed results showed that the PGTW had performed
better than the TTS. It also showed that the PGTW had very similar results
as the SGTW, but about 30{\%} CPU time is saved in the single processor
system.}}
@article{LagGlo-MS-93,
title = {{Bandwidth packing: a tabu search approach}},
author = {M. Laguna and F. Glover},
journal = {Management Science},
volume = {39},
pages = {492--500},
year = {1993},
abstract = {The bandwidth packing (BWP) problem is a combinatorially difficult
problem arising in the area of telecommunications. The problem consists
of assigning calls to paths in a capacitated graph such that capacities
are not violated and the total profit is maximized. The authors discuss
the development of a tabu search (TS) method for the BWP problem. The
method makes use of an efficient implementation of the k-shortest path
algorithm, that allows the identification of a controlled set of feasible
paths for each call. A tabu search is then performed to find the best
path assignment for each call. The TS method developed incorporates a
number of features that have proved useful for obtaining optimal and
near optimal solutions to difficult combinatorial problems. The authors
establish the effectiveness of their approach by comparing its performance
in speed and solution quality to other specialized heuristics and to
a standard optimization package applied to a 0-1 integer programming
formulation of the problem.}}
@article{LalPap-IPL-97,
title = {{Computing strictly-second shortest paths}},
author = {Kumar N. Lalgudi and Marios C. Papaefthymiou},
journal = {Information Processing Letters},
volume = {64},
number = {4},
pages = {177--181},
month = {August},
year = {1997},
note = {We investigate the problem of computing the strictly-second shortest
path connecting a given pair of vertices in a directed graph. We show
that this problem is intractable when the path is restricted to be simple.
When cycles are allowed, we give an algorithm that solves it in asymptotically
the same number of steps as it takes to compute the shortest path between
the given vertex pair.}}
@article{LalVas-GVUZPM-87,
title = {{Transformation of an oriented graph for finding the $k$ shortest
paths.}},
author = {P. I. Lalov and T. G. Vasil{\'c}eva},
journal = {Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat.},
volume = {23},
number = {4},
pages = {189--194},
year = {1987},
note = {In Bulgarian.},
review = {MR-92m-05114}}
@article{MR-92m-05114,
reviews = {LalVas-GVUZPM-87},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Transformation of an oriented graph for finding the $k$ shortest
paths.}},
volume = {92m},
number = {05114},
year = {1992},
text = {We consider an algorithm for finding the shortest simple path between
two given vertices $s$ and $t$. The algorithm is based on the Dijkstra
procedure for finding the minimal spanning tree of a graph and a graph
transformation that preserves certain paths. If this method is applied
to a graph with $m$ edges and $n$ points, there are $O(km+kn^2)$ elementary
operations.}}
@article{Law-CACM-77,
title = {{Comment on computing the $k$ shortest paths in a graph}},
author = {Eugene L. Lawler},
journal = {Commun. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {20},
pages = {603--604},
year = {1977},
abstract = {In ibid., vol.17, pp.351-3 (June 1974) Minieka presents generalizations
of the Floyd and Dantzig shortest path algorithms for the purpose of
computing the k shortest paths between all pairs of vertices in a graph.
He comments that to his knowledge no algorithm had been devised to solve
this problem.},
review = {MR-58-19354}}
@article{MR-58-19354,
reviews = {Law-CACM-77},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Comment on computing the $k$ shortest paths in a graph}},
author = {Colin J. H. McDiarmid},
volume = {58},
number = {19354},
year = {1979}}
@article{Law-MS-72,
title = {{A procedure for computing the $K$ best solutions to discrete
optimization problems and its application to the shortest path problem}},
author = {Eugene L. Lawler},
journal = {Management Science},
volume = {18},
pages = {401--405},
year = {1972},
abstract = {A general procedure is presented for computing the best, 2nd
best, $\ldots$, $K$th best solutions to a given discrete optimization
problem. If the number of computational steps required to find an optimal
solution to a problem with $n$ $(0,1)$ variables is $c(n)$, then the
amount of computation required to obtain the $K$ best solutions is $O(Knc(n))$.
The procedure specializes to published procedures of Murty (1968) and
of Yen (1971) for the assignment problem and the shortest path problem,
respectively. A method is presented for reducing the required amount
of storage by a factor of $n$, compare with the algorithms of Murty and
of Yen. It is shown how the $K$ shortest (loopless) paths in an $n$-node
network with positive and negative arcs can be computed with an amount
of computation which is $O(Kn^3)$. This represents an improvement by
a factor of $n$, compared with Yen's algorithm.},
review = {MR-45-1575}}
@article{MR-45-1575,
reviews = {Law-MS-72},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A procedure for computing the $K$ best solutions to discrete
optimization problems and its application to the shortest path problem}},
author = {J. Moravek},
volume = {45},
number = {1575},
year = {1973}}
@inproceedings{LawRez-CN-93,
title = {{Computing the $K$-shortest paths, under nonnegative weighting}},
author = {A. G. Law and A. Rezazadeh},
booktitle = {Proc. 22nd Manitoba Conf. Numerical Mathematics and Computing},
number = {92},
series = {Congr. Numer.},
pages = {277--280},
year = {1993}}
@article{LecRen-ZOR-90,
title = {{$k$-best constrained bases of a matroid}},
author = {M. Leclerc and F. Rendl},
journal = {Zeitschrift f{\"u}r Operations Research},
volume = {34},
pages = {79--89},
year = {1990},
review = {MR-91h-05039}}
@article{MR-91h-05039,
reviews = {LecRen-ZOR-90},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{$k$-best constrained bases of a matroid}},
author = {Donald M. Topkis},
volume = {91h},
number = {05039},
year = {1991},
text = {This paper considers the problem of finding the $k$-best bases
of a matroid, where the bases are required to satisfy certain partition-like
constraints. A valid algorithm is presented, and its worst-case running
time is given.}}
@inproceedings{LeeLeeCho-ICRA-95,
title = {{A real time traffic control scheme for a multiple AGV system}},
author = {J.-H. Lee and B. H. Lee and M. H. Choi and J. D. Kim and K.-T.
Joo and H. Park},
booktitle = {Int. Conf. Robotics and Automation},
publisher = {IEEE},
volume = {2},
pages = {1625--1630},
year = {1995},
abstract = {The conflict-free minimum-time motion planning problem in a
multiple AGV system using zone control requires a traffic control scheme
based upon a non-search technique, since the number of nodes contained
in the network model for its guidepath is considerably large. The traffic
control scheme presented in this paper partitions the overall task into
two constituent tasks of path generation and traffic control. The Path
Generator employs a k-shortest path search algorithm to construct path
sets between all possible station node pairs. The path generation process
is performed in off-line. Occupation times for each link are calculated
and stored in a link occupation table which is represented from a link-oriented
viewpoint. The traffic controller examines the link occupation table
and dispatches AGVs in a conflict-free minimum-time path. The on-line
motion planning operation is performed in real time.}}
@article{LeeLeeCho-SMC-98,
title = {{A real-time traffic control scheme of multiple AGV systems for
collision free minimum time motion: A routing table approach}},
author = {J.-H. Lee and B. H. Lee and M. H. Choi},
journal = {Trans. Systems, Man, and Cybernetics},
publisher = {IEEE},
volume = {28},
number = {3},
pages = {347--358},
month = {May},
year = {1998},
abstract = {A two-staged traffic control scheme, in which sets of candidate
paths are prepared off-line prior to overall motion planning process,
has been widely adopted for motion planning of mobile robots, but relatively
little attention has been given to the application of the two staged
scheme to multiple automated guided vehicle systems (MAGVS's). In this
paper, a systematic two-staged traffic control scheme is presented to
obtain collision-free minimum-time motions of AGV's along loopless paths.
The overall structure of the controller is divided into two tandem modules
of off-line routing table generator (RTG) and an on-line traffic controller
(OTC). First, an induced network model is established considering the
configurational restrictions off guide-paths. With this model and a modified
k-shortest path algorithm, RTG finds sets of k candidate paths from each
station nodes to all the other station nodes off-line and stores them
in the form of routing tables. Each time a dispatch command for an AGV
is issued, OTC utilizes these routing tables to generate a collision-free
minimum-time motion along a loopless path. Realtime computation is guaranteed
in that time-consuming graph searching process is executed off-line by
RTG, and OTC looks for the minimum time motion among the k candidate
paths. The traffic control scheme proposed is suitable for practical
application in centralized MAGVS with zone blocking technique.}}
@article{LeeWu-IEICE-99,
title = {{A $K$-best paths algorithm for highly reliable communication
networks}},
author = {Shi-Wei Lee and Cheng-Shong Wu},
journal = {IEICE Trans. Communications},
volume = {E82-B},
number = {4},
pages = {586--590},
month = {April},
year = {1999},
url = {http://search.ieice.org/1999/pdf/e82-b_4_575.pdf},
abstract = {In highly reliable communication network design, disjoint paths
between pairs of nodes are often needed in the design phase. The problem
of finding k paths which are as diverse as possible and have the lowest
total cost is called a k-best paths problem. We propose an algorithm
for finding the k-best paths connecting a pair of nodes in a graph G.
Graph extension is used to transfer the k-best paths problem to a problem
which deposits well-known maximum flow (MaxFlow) and minimum cost network
flow (MCNF) algorithms. We prove the k-best paths solution of our algorithm
to be an optimal one and the time complexity is the same as the MCNF
algorithm. Our computational experiences show that the proposed algorithm
can solve the k-best paths problem for a large network within reasonable
computation time.}}
@article{LeiAliEze-CIE-86,
title = {{A branch-and-bound algorithm for implementing set covering model
expert systems}},
author = {W. Leigh and D. Ali and C. Ezell and N. Paz},
journal = {Computers and Industrial Engineering},
volume = {11},
pages = {464--467},
year = {1986},
abstract = {The conventional rule-based expert system can be formulated
as a 0-1 integer program, specifically as a set covering problem. However,
the implementation of an expert system in this way requires that the
set covering model be solved for k-best alternate optima or near-optima.
The authors have devised a branch-and-bound algorithm which accomplishes
this. The details of the algorithm are explained in the paper. Computational
results are provided.}}
@inproceedings{LeoOda-RTERC-93,
title = {{A realtime algorithm for finding the $k$ shortest paths minimizing
travel time and right turns}},
author = {John Leo and Toshihiko Oda},
booktitle = {Proc. 13th Road Traffic Engineering Research Conf.},
publisher = {Japan Soc. for Road Traffic Engineering Research},
pages = {133--136},
month = {November},
year = {1993},
comment = {From http://www.halfaya.org/leo/interests/writing/technical.html:
``An extended abstract in English of part of this paper used to be available
via anonymous ftp from theory.lcs.mit.edu, but it has been removed. Contact
me via email [jleo@us.oracle.com] if you'd like a copy. Note however
that the version of this algorithm that handles simple paths (which is
unfortunately the most interesting version) is incorrect. This was pointed
out to me by David Staepelaere at UC Santa Cruz. There doesn't seem to
be a good fix. Send me email if you'd like more information.''},
note = {In Japanese}}
@article{LiaShe-PC-97,
title = {{Finding the $k$ most vital edges in the minimum spanning tree
problem}},
author = {Wei Fa Liang and X. J. Shen},
journal = {Parallel Computing},
volume = {23},
number = {13},
pages = {1889--1907},
month = {December},
year = {1997},
note = {Let G(V, E) be a weighted, undirected, connected simple graph with
n vertices and m edges. The k most vital edge problem with respect to
a minimum spanning tree is to find a set S(subset of or equal to E) of
k edges in G whose removal results in the greatest increase in the weight
of the minimum spanning tree in the remaining graph G(V, E - S). Although
for arbitrary k, Frederickson et al. have shown that this problem is
NP-hard, it is polynomial time solvable when k is fixed. In this paper
we introduce a sparse, weighted k-edge connected certificate of a graph
which has been found very useful, By using this certificate, we first
present a general algorithm for the problem above, Then, for a fixed
k {$>$} 1, we present efficient sequential and parallel algorithms. Our
sequential algorithm runs in time O(n(k + 1)). Our parallel algorithm
runs in time O(log n loglog n) using O(n(k + 1)) processors on an EREW
PRAM. If the minimum spanning tree of G and the sparse, weighted (k +
1)-edge connected certificate of G are given, the algorithm runs in time
O(log n) using O(n(k + 1)) processors on the same model. Particularly,
when k = 1, we develop parallel algorithms which require O(log n loglog
n) time using O(m + n(2)/(log n loglog n)) processors on an EREW PRAM,
and O(log n loglog n) time using O(m) processors on a CREW PRAM respectively,
and the algorithm on the EREW PRAM is the fastest, compared with previous
known algorithms.}}
@article{Lib-AOR-99,
title = {{On accuracy of solutions for discrete optimization problems with
perturbed coefficients of the objective function}},
author = {Marek Libura},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
volume = {86},
pages = {53--62},
year = {1999},
abstract = {An approach to the sensitivity analysis for discrete optimization
problems with perturbed objective function is presented. The problem
is stated in the following general form: min( Sigma_{e in Y} c(e):Y in
F), where c=(c(e), e in E) is a vector of weights for some finite set
E, and F contained in 2{$^\wedge$}E is a given family of feasible subsets. It is
assumed that the set of feasible solutions F is fixed, but the coefficients
of the vector c may vary. The main problem considered in this paper concerns
the following question: How does the maximum relative error of a given
feasible solution depend on inaccuracies of the problem data? Two particular
perturbations of the vector c are considered: (i) it is assumed that
c is in a closed ball with radius delta \ge 0 and center c{$^\wedge$}0\ge 0 or
(ii) the relative deviation of c(e) from the value c{$^\wedge$}0(e) is not greater
than delta for any e in E, i.e., |c(e)-c{$^\wedge$}0(e)|\le delta c{$^\wedge$}0(e), e in
E. For a given feasible solution X in F, two functions of the parameter
delta are introduced: the sensitivity function s(X,delta) and the accuracy
function a(X,delta). The values of s(X,delta) and a(X,delta) are equal
to the maximum relative error of the solution X when the perturbations
of problem data are of the type (i) or (ii), respectively. Some general,
but computationally inefficient formulae for calculating these functions
are derived and their properties are studied. It is shown that s(X,delta)
and a(X,delta) are nondecreasing, convex functions with a limited number
of breakpoints. A practically efficient method of calculating upper and
lower envelopes for the accuracy function is presented. This method is
based on the notion of k-best solutions of the problem. It gives an interval
to which the maximum relative error of the solution X must belong when
the coefficients of vector c are given with accuracy delta . The approach
is illustrated with an example of the symmetric traveling salesman problem.}}
@inproceedings{LibPoo-ECCO-95,
title = {{On $k$-best solutions and sensitivity analysis for the traveling
salesman problem}},
author = {Marek Libura and Edo S. van der Poort},
booktitle = {ECCO VIII, Poznan, Poland, Conf. of the Eur. Chapter on Combinatorial
Optimization},
year = {1995}}
@article{LibPooSie-DAM-98,
title = {{Stability aspects of the traveling salesman problem based on
$k$-best solutions}},
author = {Marek Libura and Edo S. van der Poort and Gerard Sierksma and
Jack A. A. van der Veen},
journal = {Discrete Applied Mathematics},
volume = {87},
number = {1--3},
pages = {159--185},
month = {October},
year = {1998},
abstract = {This paper discusses stability analysis for the Traveling Salesman
Problem (TSP). For a traveling salesman tour which is known to be optimal
with respect to a given instance (length vector) we are interested in
determining the stability region, i.e. the set of all length vectors
for which the tour is optimal. The following three subsets of the stability
region are of special interest: (1) tolerances, i.e. the maximum perturbations
of single edges; (2) tolerance regions which are subsets of the stability
region that can be constructed from the tolerances; and (3) the largest
ball contained in the stability region centered at the given length vector
(the corresponding radius is known as the stability radius). It is well
known that the problems of determining tolerances and the stability radius
for the TSP are NP-hard so that in general it is not possible to obtain
the above-mentioned three subsets without spending a lot of computation
time. The question addressed in this paper is the following: assume that
not only an optimal tour is known, but also a set of k shortest tours
(k{$>$}or=2) is given. Then to which extent does this allow us to determine
the three subsets in polynomial time? It will be shown in this paper
that having k-best solutions can give the desired information only partially.
More precisely, it will be shown that only some of the tolerances can
be determined exactly and for the other ones as well as for the stability
radius only lower and/or upper bounds can be derived. Since the amount
of information that can be derived from the set of k-best solutions is
dependent on both the value of k as well as on the specific length vector,
we present numerical experiments on instances from the TSPLIB library
to analyze the effectiveness of our approach.}}
@inproceedings{LibPooSie-ISMP-97,
title = {{Sensitivity analysis for combinatorial optimization problems
based on subsets of $k$-best solutions}},
author = {Marek Libura and Edo S. van der Poort and Gerard Sierksma and
Jack A. A. van der Veen},
booktitle = {Int. Symp. Mathematical Programming},
month = {August},
year = {1997},
abstract = {We consider the combinatorial optimization problem: $\min \{
\sum_{e \in F} c(e) : F \in {\cal F} \}$, where for a given finite set
$E$, $c(e)$ denotes the weight of element $e \in E$, and $\cal F$ is
a family of feasible subsets ${\cal F} \subseteq 2^E$. Assuming that
a set of k-best solutions of this problem is known, we investigate the
possibility of solving various sensitivity analysis questions concerning
the weights of elements. We concentrate on the following problems: --
calculating so-called tolerances of weights with respect to an optimal
solution, defined as maximum individual changes of weights preserving
the optimality of this solution; -- describing the region of allowable
simultaneous changes of weights provided by tolerances of single weights;
-- computing so-called stability radius of an optimal solution, which
gives the maximum simultaneous changes of weights preserving the optimality
of this solution; -- determining the maximum relative error of a given
feasible solution as a function of accuracy of estimating the weights
of elements. We illustrate presented results with examples of the symmetric
traveling salesman problem.}}
@inproceedings{LinDav-ISCS-87,
title = {{Electrical network theory applications to optimal routing problems}},
author = {L.-M. Jin and A. C. Davies},
booktitle = {Proc. Int. Symp. Circuits {\&} Systems},
publisher = {IEEE},
volume = {1},
pages = {23--26},
month = {May},
year = {1987},
abstract = {A variety of problems of operations research can be solved
by analogies with electrical networks. In some cases, this approach appears
to offer improved solution algorithms to those conventionally used, and
in others it provides an alternative and interesting insight into the
problems and their solution. The authors illustrate these concepts by
examples of networks with negative cost branches, negative cost loops,
finding the $k^{\rm th}$ least cost routes, optimized networks in which
all routes have equal cost, and sensitivity of least cost routes to cost
variations.}}
@article{LinTse-EJOR-93,
title = {{Generating the best $K$-sequences in relocation problems}},
author = {B. M. T. Lin and S. S. Tseng},
journal = {Eur. J. Operational Research},
volume = {69},
number = {1},
pages = {131--137},
month = {August},
year = {1993},
note = {There is a set J of h jobs to be processed. For every i, job J(i)
demands n(i) units of resources and returns a(i) units after completion.
The problem is to find the best K schedules whose resource requirements
are minimum among all h! ones. In this paper, we present some important
structural properties and then propose an O(h log h + hK log K) time
algorithm, which runs in polynomial time if K is fixed.}}
@inproceedings{Liu-IEAAI-95,
title = {{Intelligent air travel and tourist information systems}},
author = {Bing Liu},
booktitle = {Proc. 8th Int. Conf. Engineering Applications of Artificial
Intelligence and Expert Systems},
publisher = {Gordon {\&} Breach},
editor = {G. F. Forsyth},
pages = {603--610},
month = {June},
year = {1995},
abstract = {Traveling and touring has become an important part of modern
life. The planning of such activities is, however, often time-consuming
and frustrating. In this paper, a prototype computer system is described
that is aimed at helping in these situations. Specifically, the system
helps in two types of planning. The first type is travel planning (i.e.
before we leave, we need to make travel arrangements). The second is
sightseeing planning (i.e. when we arrive at our destination, we need
to get some advice and to plan our sightseeing so that we can make best
use of our time there). To deal with the first problem, two modified
k-shortest path algorithms and a double search technique are proposed.
To deal with the second problem, a machine learning technique is employed
to make the system learn to give sightseeing advice. A branch-and-bound
technique is also used to sequence sightseeing activities.}}
@inproceedings{LloWriJon-ASSP-95,
title = {{An integrated grammar/bigram language model using path scores}},
author = {H. Lloyd-Thomas and J. H. Wright and G. J. F. Jones},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {173--176},
month = {May},
year = {1995},
abstract = {This paper describes a language model in which context-free
grammar rules are integrated into an $n$-gram framework, complementing
it instead of attempting to replace it. This releases the grammar from
the aim of parsing sentences overall (which is often undesirable as well
as unrealistic), enabling it to be employed selectively in modelling
phrases that are identifiable within a flow of speech. Algorithms for
model training and for sentence scoring and interpretation are described.
All are based on the principle of summing over paths that span the sentence,
but implementation is node-based for efficiency. Perplexity results for
this system (using a hierarchy of grammars from empty to full-coverage)
are compared with those for $n$-gram models, and the system is used for
re-scoring $N$-best sentence lists for a speaker-independent recogniser.}}
@article{MacGro-SPE-94,
title = {{Optimized $k$-shortest-paths algorithm for facility restoration}},
author = {M. H. MacGregor and Wayne Davy Grover},
journal = {Software Practice and Experience},
volume = {24},
number = {9},
pages = {823--834},
month = {September},
year = {1994},
abstract = {The problem of finding shortest paths arises in many contexts;
testing restoration algorithms and developing design packages for large
telecommunications networks are two cases where the simple task of finding
sets of restoration paths can consume up to 95 per cent of the execution
time of an application program. This paper presents experimental studies
of several well-known shortest-paths algorithms adapted to the task of
finding the $k$-successively-shortest link-disjoint replacement paths
for restoration in a telecommunications network with $n$ nodes. The implementations
range in complexity from $O(kn^2)$ when based on Dijkstra's original
method (1959), through several improvements to an efficient implementation
of $O(kn(v+\log{n}))$ complexity, and finally to an $O(kn)$ implementation
for the special case of edge-sparse graphs with small integer edge weights.}}
@incollection{MacSouCan-AOR-91,
title = {{An approach for the Steiner problem in directed graphs}},
author = {Nelson Maculan and Paulo Souza and Candia Vejar, Alfredo},
booktitle = {Topological Network Design},
number = {33},
editor = {J. MacGregor Smith and P. Winter},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
pages = {471--480},
year = {1991},
review = {MR-92h-90051}}
@article{MR-92h-90051,
reviews = {MacSouCan-AOR-91},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An approach for the Steiner problem in directed graphs}},
volume = {92h},
number = {90051},
year = {1992},
text = {We present a scheme to solve the Steiner problem in directed graphs
using a heuristic method to obtain upper bounds and the $k$ shortest
arborescences algorithm to compute lower bounds. We propose to combine
these ideas in an enumerative algorithm. Computational results are presented
for both the $k$ shortest arborescenses algorithm and the heuristic method,
including reduction tests for the problem.}}
@inproceedings{MahHuZil-CSOR-92,
title = {{Implementation and testing of a $K$-shortest path algorithm in
a vector and parallel processing environment}},
author = {Ta-Yin Hu and Hani S. Mahmassani and Athanasios Kostantine Ziliaskopoulos},
booktitle = {Proc. Conf. Computer Science {\&} Operations Research: New Developments
{\&} their Interfaces},
month = {January},
year = {1992}}
@inproceedings{MaIwaGu-AIZU-97,
title = {{A parallel algorithm for $k$-minimum spanning trees}},
author = {Jun Ma and K. Iwama and Qian-Ping Gu},
booktitle = {Proc. 2nd AIZU Int. Symp. Parallel Algorithms/Architecture
Synthesis},
publisher = {IEEE},
pages = {384--388},
month = {March},
year = {1997},
abstract = {A parallel algorithm to find $k$, $2\le k\le n^{n-2}$, spanning
trees from a connected, weighted and undirected graph C(V, E, W) in the
order of increasing weight is presented. It runs in $O(T(n)+k\log n)$
time with $O(n^2\log n)$ processors on a CREW PRAM, where $n=|V|$, $m=|E|$
and $T(n)$, $O(\log n)\le T(n)\le O(\log^2 n)$, is the time of the fastest
parallel algorithms to find a minimum spanning tree of G on a CREW PRAM
with no more than $O(n^2\log n)$ processors. Since $T(n)=O(\log^2 n)$
for the time being, this result shows that to find $k$ minimum spanning
trees can be done in the same time bound as to find just one when $k\le
O(\log n)$ on a CREW PRAM.}}
@article{MalMitGup-ORL-89,
title = {{The $k$ most vital arcs in the shortest path problem}},
author = {K. Malik and A. K. Mittal and S. K. Gupta},
journal = {Operations Research Lett.},
volume = {8},
pages = {223--227},
year = {1989},
abstract = {The k most vital arcs in a network are those whose removal
from the network results in the greatest increase in the shortest distance
between two specified nodes. An exact algorithm is proposed to determine
the k most vital arcs. Furthermore, an algorithm of time complexity equal
to that of Dijkstra's algorithm for the shortest path problem is developed
to solve the single most vital arc problem.}}
@inproceedings{MamBer-PES-78,
title = {{Alternative long-range expansion plans for transmission systems}},
author = {K. R. C. Mamandur and G. J. Berg},
booktitle = {Power Engineering Soc., Winter Mtg.},
publisher = {IEEE},
pages = {042-4/1-6},
year = {1978},
abstract = {Presents a long range transmission expansion planning technique
which gives k-best policies for the transmission system expansion, k
being specified by the planner. The objective is to minimize the net
present value of the capital investment cost associated with the construction
of new transmission facilities. The approach is based on an efficient
algorithm for finding k-shortest loopless paths (k{$>$}or=1) from one node
in a network to another. A minimum number of feasible expansion alternatives
are determined at every stage, and the first, second, third, etc., optimal
expansion plans are subsequently identified. Application of the method
to a simple network is illustrated.}}
@article{Mar-EJOR-84,
title = {{An algorithm for ranking paths that may contain cycles}},
author = {Ernesto de Queir{\'o}s Vieira Martins},
journal = {Eur. J. Operational Research},
volume = {18},
number = {1},
pages = {123--130},
year = {1984},
review = {MR-85j-05030}}
@article{MR-85j-05030,
reviews = {Mar-EJOR-84},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An algorithm for ranking paths that may contain cycles}},
author = {Takao Ozawa},
volume = {85j},
number = {05030},
year = {1985},
text = {In order to find the $K$ best paths in a directed network, a sequence
of networks $G\sb 1,\cdots,G\sb i,G\sb {i+1},\cdots,G\sb K$ is constructed,
where $G\sb 1$ is the given network and $G\sb {i+1}$ is derived from
$G\sb i$ in such a way that only the best path in $G\sb i$ is eliminated.
The elimination procedure of the best path $p\sb i=\{s\sb 1,(s\sb 1,s\sb
2),s\sb 2,\cdots,s\sb {m-1}, (s\sb {m-1},s\sb m),s\sb m\}$ in $G\sb i$
in the case of $m>2$ is as follows.
Step 1: Delete arc $(s\sb {m-1},s\sb m)$ from $G\sb i$.
Step 2: For node $s\sb j$ $(j=2,\cdots,m-1)$ in $G\sb i$ adjoin node
$s'\sb j$.
Step 3: For every arc $(x,s\sb j)$ $(j=2,\cdots,m-1)$ in $G\sb i$ adjoin
arc $(x,s'\sb j)$.
Step 4: For $j=2,\cdots,m-2$ adjoin arc $(s'\sb j,s'\sb {j+1})$.
Step 5: Adjoin arc $(s'\sb {m-1},s\sb m)$.
The best path in $G\sb i$ for $i=1,2,\cdots,K$ may be obtained by any
existing shortest path algorithm. Computational results are presented
and comparisons with Dreyfus' algorithms and the double-sweep method
of Shier are made. As for the computational time the proposed approach
is never the worst, and never the best. The memory space required is
smaller. The approach can be used for ranking paths under a nonlinear
objective function.}}
@article{Mar-IEICE-93,
title = {{A new $k$th-shortest path algorithm}},
author = {H. Maruyama},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E76-D},
number = {3},
pages = {388--389},
month = {March},
year = {1993},
abstract = {An algorithm is presented for finding the kth-shortest paths
between a specified pair of vertices in a directed graph with arcs having
nonnegative costs. The kth-shortest path problem is to find the shortest,
the second shortest, the third shortest, . . and the kth-shortest paths
from the origin vertex s to the target vertex t. Paths may contain repeated
vertices. Two paths are considered distinct if they do not visit precisely
the same vertices in the same order. Under certain conditions, the algorithm
is faster than Dreyfus' algorithm (S.C. Dreyfus, 1969).}}
@article{Mar-ORS-83,
title = {{An algorithm for ranking paths in acyclic networks}},
author = {Ernesto de Queir{\'o}s Vieira Martins},
journal = {Operations Research Spektrum},
volume = {5},
pages = {87--90},
year = {1983},
abstract = {The algorithm is initialised with the determination of the
shortest tree which is placed in a candidate List. At each step the tree
for which the distance of the path between two specified nodes is minimal
is removed from List. Some adjacent trees of the removed one are generated
and placed in List in such a way that repetitions are avoided. This method
is repeated until the desired paths have been determined. The computational
complexity of the algorithm is studied too.}}
@inproceedings{MarFohAug-ICSLP-94,
title = {{Hidden Markov models and selectively trained neural networks
for connected confusable word recognition}},
author = {J.-F. Mari and D. Fohr and Y. Auglade and Jean-Claude Junqua},
booktitle = {Proc. Int. Conf. Spoken Language Processing},
publisher = {Acoustical Soc. Japan},
volume = {3},
pages = {1519--1522},
month = {September},
year = {1994},
abstract = {This paper presents a new method for connected-word recognition
with confusable vocabularies, such as connected letters. The recognition
process is performed in two steps. First, a second-order HMM provides
$N$-best word strings. Then, the strings of confusable letters are discriminated
by a procedure based on acoustic knowledge and artificial neural networks
(ANN). This method has been tested on an American-English database containing
spelled names collected through the telephone network. The results obtained
with the first HMM pass and the improvements made with the ANN are presented
and discussed. When a 3,300 name dictionary and a retrieval procedure
based on a DTW alignment algorithm were used, 96{\%} recognition accuracy
was obtained.}}
@techreport{MarJim-TR-92,
title = {{A comparative study of classical algorithms and new approaches
for the search of the $K$ best paths in a graph}},
author = {Marzal Var{\'o}, Andr{\'e}s and Jim{\'e}nez Pelayo, V{\'\i}ctor Manuel},
institution = {Univ. Polit{\'e}cnica de Valencia, Spain, Dep. Sist. Inform{\'a}ticos
y Computaci{\'o}n},
number = {DISC-II/28/92},
year = {1992}}
@article{MarNie-CGTA-01,
title = {{Enumerating the $k$ best plane spanning trees}},
author = {Ambros Marzetta and Jurg Nievergelt},
journal = {Computational Geometry Theory and Applications},
volume = {18},
number = {1},
pages = {55--64},
month = {February},
year = {2001},
abstract = {A spanning tree constructed of straight line segments over
a set of points in the Euclidean plane is called ``non-crossing'' or ``plane
tree'', if no two segments intersect. Imposing the additional constraint
of non-crossing segments makes many combinatorial geometric problems
harder. In the case of plane spanning trees, however, we show that they
can be enumerated efficiently in the order of their total length. This
makes it possible to efficiently find the $k$ best plane trees, or all
those shorter than a given bound.}}
@article{MarPasSan-IJFCS-99,
title = {{Deviation algorithms for ranking shortest paths}},
author = {Ernesto de Queir{\'o}s Vieira Martins and Marta Margarida Braz Pascoal
and Jos{\'e} Lu{\'\i}s Esteves dos Santos},
journal = {Int. J. Found. Comp. Sci.},
volume = {10},
number = {3},
pages = {247--263},
year = {1999},
url = {http://www.mat.uc.pt/~eqvm/cientificos/investigacao/Artigos/deviation.ps.gz}}
@inproceedings{MarVid-ICPR-92,
title = {{A $N$ best sentence hypotheses enumeration algorithm with duration
constraints based on the two level algorithm}},
author = {Marzal Var{\'o}, Andr{\'e}s and E. Vidal},
booktitle = {Proc. 11th Int. Conf. Pattern Recognition},
publisher = {IEEE},
year = {1992}}
@article{Mat-Algo-97,
title = {{A flexible algorithm for generating all the spanning trees in
undirected graphs}},
author = {Tomomi Matsui},
journal = {Algorithmica},
volume = {18},
number = {4},
pages = {530--543},
month = {August},
year = {1997},
abstract = {In this paper we propose an algorithm for generating all the
spanning trees in undirected graphs. The algorithm requires $O(n+m+\tau
n)$ time where the given graph has $n$ vertices, $m$ edges, and $\tau$
spanning trees. For outputting all the spanning trees explicitly, this
time complexity is optimal.
Our algorithm follows a special rooted tree structure on the skeleton
graph of the spanning tree polytope. The rule by which the rooted tree
structure is traversed is irrelevant to the time complexity. In this
sense, our algorithm is flexible.
If we employ the depth-first search rule. we can save the memory requirement
to $O(m+\tau n)$. A breadth-first implementation requires as much as
$O(nr+\tau n)$ space, but when a parallel computer is available, this
might have an advantage. When a given graph is weighted, the best-first
search rule provides a ranking algorithm for the minimum spanning tree
problem. The ranking algorithm requires $O(n + m + \tau n)$ time and
$O(m + \tau n)$ space when we have a minimum spanning tree.}}
@techreport{Mat-TR-93,
title = {{An algorithm for finding all the spanning trees in undirected
graphs}},
author = {Tomomi Matsui},
institution = {Univ. of Tokyo, Dept. of Mathematical Engineering and Information
Physics},
number = {METR93-08},
year = {1993},
abstract = {In this paper we propose an algorithm for generating all the
spanning trees in undirected graphs. The algorithm requires $O(n+m+\tau
n)$ time and $O(n+m)$ space where the given graph has $n$ vertices, $m$
edges, and $\tau$ spanning trees. For outputting all the spanning trees
explicitly, this algorithm is optimal.}}
@inproceedings{MatMatUno-ISORA-95,
title = {{Finding all the $s$-$t$ paths in acyclic graphs}},
author = {Yasuko Matsui and Tomomi Matsui and Takeaki Uno},
booktitle = {Proc. 1st Int. Symp. Operations Research and Its Applications},
publisher = {Beijing World Publishing},
editor = {Ding-Zhu Du and X.-S. Zhang},
pages = {259--266},
month = {August},
year = {1995},
abstract = {We discuss the problem of finding all the $s$-$t$ paths in
acyclic graphs under three restrictions and present three enumeration
algorithms. We propose the following three algorithms: an algorithm for
finding all the $s$-$t$ paths in acyclic graph; an algorithm for finding
all the $s$-$t$ shortest paths in directed graphs whose edge set has
a positive length function; and an algorithm for finding all the optimum
solutions of the 0-1 knapsack problems.}}
@article{MatTamIke-DAM-94,
title = {{Algorithms for finding a $K$th best valued assignment}},
author = {Tomomi Matsui and A. Tamura and Y. Ikebe},
journal = {Discrete Applied Mathematics},
volume = {50},
number = {3},
pages = {283--296},
year = {1994},
review = {MR-95e-90051}}
@article{MR-95e-90051,
reviews = {MatTamIke-DAM-94},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Algorithms for finding a $K$th best valued assignment}},
volume = {95e},
number = {90051},
year = {1995},
text = {We consider a new problem, the $K$th best valued assignment problem.
Given a bipartite graph $G$ and a cost vector $w$ on its edge set, this
is the problem of finding a perfect matching $M\sb K$ in $G$ such that
there exist perfect matchings $M\sb 1,\cdots,M\sb {K-1}$ satisfying $w(M\sb
1)<\cdots$}= 0 for all k and l if and only if X{sup}0
is an optimal solution of the assignment problem. If this necessary and
sufficient condition is fulfilled, a minimal F{sub}(kl) may be determined.
By the definition of c{sup}((k)){sub}(ij) this can be written in the
form F {sub}(kl)={sum}{sub}(i=1){sup}n 3{sum}{sub}(j=1){sup}n 3c{sub}(ij)u{sub}(ij);
X{sup}0+U is an optimal solution of PSBA (U=(u{sub}(ij))). The algorithm
requires at most 7n{sup}3/6 arithmetic operations.}}
@techreport{MilStoCox-TR-95,
title = {{Optimizing Murty's ranked assignment method}},
author = {Matt L. Miller and Harold S. Stone and Ingemar J. Cox},
address = {4 Independence Way, Princeton, NJ 08540, USA},
organization = {NEC Research Inst.},
number = {95-08},
year = {1995},
url = {http://www.neci.nj.nec.com/tr/neci-tr-95-8.ps},
abstract = {We describe an implementation of an algorithm due to Murty
for determining a ranked set of solutions to assignment problems. The
intended use of the algorithm is in the context of multi-target tracking,
where it has been shown that real-time multi-target tracking is now feasible,
but many other uses of the algorithm are also possible. Three optimizations
are discussed: (1) inheriting dual variables and partial solutions during
partitioning, (2) sorting subproblems by lower cost bounds before solving
and (3) partitioning in an optimized order. When used to find the 100
best solutions to random 100x100 assignment problems, these optimizations
produce a speedup of over a factor of 20, finding all 100 solutions in
about 0:6 seconds. For a random cost matrix, the average time complexity
for finding k solutions to random NxN problems appears to be nearly linear
in both k and N , for sufficiently large k.}}
@article{Min-CACM-74,
title = {{On computing sets of shortest paths in a graph}},
author = {Edward Minieka},
journal = {Commun. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {17},
pages = {351--353},
year = {1974},
abstract = {Two algorithms are presented that construct the k shortest
paths between every pair of vertices in a directed graph. These algorithms
generalize the Floyd algorithm and the Dantzig algorithm for finding
the shortest path between every pair of vertices in a directed graph.}}
@inproceedings{Min-JNM-75,
title = {{The $K$-th shortest path problem}},
author = {Edward Minieka},
booktitle = {ORSA/TIMS Joint National Mtg.},
journal = {Bull. Operations Research Soc. of America},
volume = {23},
pages = {B/116},
year = {1975},
abstract = {This paper presents a short graph theoretical proof for the
Jacobi, Gauss-Seidel and Double Sweep Algorithms for finding the K shortest
paths from a given vertex to each other vertex. This proof is valid for
any starting solution that exceeds the optimal solution.}}
@article{MinShi-JIMA-73,
title = {{A note on an algebra for the $k$ best routes in a network}},
author = {Edward Minieka and Douglas R. Shier},
journal = {J. Inst. Mathematics and Its Applications},
volume = {11},
pages = {145--149},
year = {1973},
abstract = {This note extends the general algebraic theory of network routing
problems to the problem of finding the k best routes in a network. Techniques
for solving linear equations in this extended algebra produce corresponding
algorithms for determining the k best routes.},
review = {MR-48-13216}}
@article{MR-48-13216,
reviews = {MinShi-JIMA-73},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A note on an algebra for the $k$ best routes in a network}},
author = {G. Berman},
volume = {48},
number = {13216},
year = {1974}}
@article{MirArj-IPL-85,
title = {{Selection in $X+Y$ and matrices with sorted rows and columns}},
author = {Andranik Mirzaian and E. Arjomandi},
journal = {Information Processing Letters},
volume = {20},
number = {1},
pages = {13--17},
year = {1985}}
@article{Mis-ETED-81,
title = {{Connection matrix approach for global reliability path enumeration}},
author = {R. B. Misra},
journal = {J. Inst. Engineers (India) Electronics and Telecommunication
Engineering Division},
volume = {61},
pages = {ET3:74--76},
year = {1981},
abstract = {An algorithm for enumeration of all simple paths for global
reliability in a communication network is presented. The paths are enumerated
with the help of incidence and connection matrices of the graph. The
method is also applicable to networks having both nodes and branches
of finite failure probability. The efficiency of the method increases
with the complexity of the network and is best suitable for networks
having both nodes and branches unreliable. A computer program for implementation
of the algorithm is also developed.}}
@article{Mis-MR-79,
title = {{An algorithm for enumerating all simple paths in a communication
network}},
author = {R. B. Misra},
journal = {Microelectronics and Reliability},
volume = {19},
number = {4},
pages = {363--366},
year = {1979},
abstract = {A more efficient algorithm of path enumeration for global reliability
evaluation of a communication network is presented and analyzed. The
paths are generated from the incidence matrix of the graph. This new
algorithm seems to be promising in respect to existing methods both for
computation time and computer memory requirement.}}
@article{MisMis-MR-80,
title = {{Enumeration of all simple paths in a communication network}},
author = {R. B. Misra and K. B. Misra},
journal = {Microelectronics and Reliability},
volume = {20},
pages = {419--426},
year = {1980},
abstract = {An algorithm has been developed for enumerating all simple
paths in a communication network for specified terminal pairs. The efficiency
of the method increases with the number of terminal pairs for which path
enumeration is required. The algorithm generates the paths in ascending
order of cardinality. The method is applicable to the graphs having finite
non zero failure probability nodes. A FORTRAN program for implementation
of the algorithm has been developed and results are reported.}}
@article{MotMurOls-EJOR-91,
title = {{A parametric approach to solving bicriterion shortest path problems}},
author = {J. Mote and I. Murthy and D. L. Olson},
journal = {Eur. J. Operational Research},
volume = {53},
number = {1},
pages = {81--92},
month = {July},
year = {1991},
abstract = {A new algorithm is developed to solve bicriterion shortest
path problems (BSP). This algorithm first relaxes the integrality conditions
and solves a simple bicriterion network problem. The bicriterion network
problem is solved parametrically, exploiting properties associated with
adjacent basis trees. Those Pareto-optimal paths not obtained by solving
the LP relaxation are obtained using a label correcting procedure. Computational
results comparing the parametric approach to the label setting approach
and the K-th shortest path approach are also presented.}}
@inproceedings{MouJouMon-ASSP-95,
title = {{On using a priori segmentation of the speech signal in an $N$-best
solutions post-processing}},
author = {T. Moudenc and D. Jouvet and J. Monne},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {580--583},
month = {May},
year = {1995},
abstract = {This paper proposes a new approach to the incorporation of
automatic a-priori segmentation into an HMM based speech recognizer.
The approach used for the post-processing of $N$-best solutions is based
on stochastic modelling of the number of speech signal stationarity changes
which occur within the phonetic segments of each solution. The objective
of this post-processing is to validate the presence of stationarity zones
in the speech signal. This particular validation cannot be exploited
using a centisecond approach. The signal stationarity changes are detected
using an ``a priori'' segmentation algorithm. Two phonetic models are calculated
for each phonetic segment. One corresponds to correct solutions and the
other one corresponds to incorrect solutions. These two models are used
simultaneously in order to compute a post-processing score for each solution.
In the initial set of experiments, which was conducted on telephone databases,
the use of this method resulted in a 9{\%} error rate reduction on the ``Number''
database, and a 15{\%} error rate reduction on the ``Digit'' database.}}
@article{Mur-OR-68,
title = {{An algorithm for ranking all the assignments in order of increasing
costs}},
author = {K. G. Murty},
journal = {Operations Research},
volume = {16},
pages = {682--687},
year = {1968}}
@phdthesis{Mur-PhD-95,
title = {{Survivable Network Management for High-Speed ATM Networks}},
author = {Kazutaka Murakami},
school = {Carnegie Mellon University},
year = {1995},
abstract = {Fast restoration from a network failure has been recognized
as a key ingredient in realizing survivable networks in emerging high-speed
ATM environments. Self-healing techniques have been proposed to provide
service continuity to end-users by autonomously switching affected virtual
paths to alternate routes. However, their success greatly depends on
how traffic is distributed and spare capacity is dimensioned over the
network when a failure occurs. Therefore, a fast restoration mechanism
alone is not enough to achieve a high level of survivability. This dissertation
aims at defining an integrated framework for survivable ATM network management
ranging from network design and virtual path management to fast restoration
protocol. The focus is placed on two aspects essential to promoting restoration
capability: the survivable virtual path routing (SVPR) and the survivable
capacity and flow assignment (SCFA). The SVPR attempts to maximize restorability
from a possible network failure by adjusting virtual path configuration
in response to a change in traffic demand or facility network configuration.
The two-step restoration concept is also introduced to achieve fast restoration
as well as optimal reconfiguration. The SCFA seeks for the most economical
physical link capacity placement in order to deploy a survivable network
in a cost-effective manner. Joint optimization is carried out to find
a globally optimal solution. The problems for maximum-flow restoration-based
networks are formulated as a large-scale linear programming model. Several
mechanisms are devised to reduce computation time by facilitating the
basis matrix factorization. The SVPR for k-shortest path restoration-based
networks is modeled as a non-smooth multicommodity flow problem with
linear constraints. A modified flow deviation method is developed to
obtain a near-optimal solution in a reasonable computation time. Premature
convergence to a non-smooth point is avoided by properly adjusting optimization
parameters. Using the proposed optimization procedures, the minimum resource
installation cost is quantitatively analyzed for different fast restoration
schemes. Contrary to a wide belief in the economic advantage of the end-to-end
restoration scheme, this study reveals that the attainable gain could
be marginal for a well-connected and/or unbalanced network.}}
@inproceedings{Nag-ICSLP-94,
title = {{A stochastic morphological analyzer for spontaneously spoken
languages}},
author = {M. Nagata},
booktitle = {Proc. Int. Conf. Spoken Language Processing},
publisher = {Acoustical Soc. Japan},
volume = {2},
pages = {795--798},
month = {September},
year = {1994},
abstract = {We present a morphological analysis method for the phonetic
transcription of spontaneous speech using a stochastic language modeling
technique and an efficient two-pass $N$-best search strategy. It can
segment a phonetically transcribed utterance into word, assign parts
of speech to each segmented words, and convert the phonetic transcription
into an orthographic transcription, which, in the case of Japanese, means
the conversion from ``hiragana'' (phonogram) to ``kanji'' (ideogram). The
morphological analyzer can handle pauses, interjections, restatements
and chimings, all which are characteristics of spontaneous speech, by
learning the parameters of the language model directly from the phonetic
transcription. The proposed morphological analyzer achieves 95.0{\%} recall
and 95.3{\%} precision on closed text when it was trained and tested on
a portion (containing 172,826 words) of the ATR Corpus, telephone dialogues
in the conference registration domain.}}
@inproceedings{NagNisIba-ISAAC-94,
title = {{Computing all small cuts in undirected networks}},
author = {H. Nagamochi and K. Nishimura and Toshihide Ibaraki},
booktitle = {Proc. 5th Int. Symp. Algorithms and Computation},
number = {834},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {190--198},
year = {1994},
abstract = {Let $\lambda(N)$ denote the weight of a minimum cut in an edge-weighted
undirected network $N$, where $n$ and $m$ are the numbers of vertices
and edges, respectively. It is known that $O(n^2k)$ is an upper bound
on the number of cuts with weights less than $k\lambda(N)$. We first
show that all cuts of weights less than $k\lambda(N)$ can be enumerated
in$O(mn^3+n^2k+2)$ time without using the maximum flow algorithm. We
then prove for $k<4/3$ that $n\choose 2$ is a tight upper bound on the
number of cuts of wights less than $k\lambda(N)$.}}
@inproceedings{NakShi-ICSLP-94,
title = {{Accent phrase segmentation by finding $N$-best sequences of pitch
pattern templates}},
author = {M. Nakai and H. Shimodaira},
booktitle = {Proc. Int. Conf. Spoken Language Processing},
publisher = {Acoustical Soc. Japan},
volume = {1},
pages = {347--350},
month = {September},
year = {1994},
abstract = {This paper describes a prosodic method for segmenting continuous
speech into accent phrases. Optimum sequences are obtained on the basis
of least squared error criterion by using dynamic time warping between
$F_0$ contours of input speech and reference accent patterns called `pitch
pattern templates'. But the optimum sequence does not always give good
agreement with phrase boundaries labeled by hand, while the second or
the third optimum candidate sequence does well. Therefore, we expand
our system to be able to find out multiple candidates by using $N$-best
algorithm. Evaluation tests were carried out using the ATR continuous
speech database of 10 speakers. The results showed about 97{\%} of phrase
boundaries were correctly detected when we took 30-best candidates, and
this accuracy is 7.5{\%} higher than the conventional method without using
$N$-best search algorithm.}}
@inproceedings{NakSinSag-ASSP-95,
title = {{Automatic prosodic segmentation by $F_0$ clustering using superpositional
modeling}},
author = {M. Nakai and H. Singer and Y. Sagisaka and H. Shimodaira},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {624--627},
month = {May},
year = {1995},
abstract = {In this paper, we propose an automatic method for detecting
accent phrase boundaries in Japanese continuous speech by using $F_0$
information. In the training phase, hand labeled accent patterns are
parameterized according to a superpositional model proposed by Fujisaki,
and assigned to some clusters by a clustering method, in which accent
templates are calculated as centroid of each cluster. In the segmentation
phase, automatic $N$-best extraction of boundaries is performed by one-stage
DP matching between the reference templates and the target $F_0$ contour.
About 90{\%} of accent phrase boundaries were correctly detected in speaker
independent experiments with the ATR Japanese continuous speech database.}}
@inproceedings{NaoBru-CPM-93,
title = {{On suboptimal alignments of biological sequences}},
author = {Dalit Naor and Douglas Brutlag},
booktitle = {Proc. 4th Symp. Combinatorial Pattern Matching},
number = {684},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {179--196},
year = {1993},
url = {http://cmgm.stanford.edu/~brutlag/Publications/naor93.html},
review = {MR-94i-92013}}
@article{MR-94i-92013,
reviews = {NaoBru-CPM-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On suboptimal alignments of biological sequences}},
volume = {94i},
number = {92013},
year = {1994},
text = {It is widely accepted that the optimal alignment between a pair
of proteins or nucleic acid
sequences that minimizes the edit distance may not necessarily reflect
the correct biological alignment. Alignments of proteins based on their
structures or of DNA sequences based on evolutionary changes are often
different from alignments that minimize edit distance. However, in many
cases (e.g. when the sequences are close), the edit distance alignment
is a good approximation to the biological one. Since, for most sequences,
the true alignment is unknown, a method that either assesses the significance
of the optimal alignment, or that provides few `close' alternatives to
the optimal one, is of great importance.
A suboptimal alignment is an alignment whose score lies within the neighborhood
of the optimal score. Enumeration of suboptimal alignments is not very
practical since there are many such alignments. Other approaches that
use only partial information about suboptimal alignments are more successful
in practice.
We present a method for representing all alignments whose score is within
any given delta from the optimal score. It represents a large number
of alignments by a compact graph which makes it easy to impose additional
biological constraints and select one desirable alignment from this large
set. We study the combinatorial nature of suboptimal alignments. We define
a set of `canonical' suboptimal alignments, and argue that these are
the essential ones since any other suboptimal alignment is a combination
of few canonical ones. We then show how to efficiently enumerate suboptimal
alignments in order of their score, and count their numbers. Examples
are presented to motivate the problem.
Since alignments are essentially $(s,t)$-paths in a directed acyclic
graph with (possibly negative) weights on its edges, our solution gives
an extremely simple method to enumerate all $K$ shortest (or longest)
paths from $s$ to $t$ in such graphs in increasing order, as well as
all $(s,t)$ paths that are within $\delta$ of the optimum, for any $\delta$.
We compare this solution with known algorithms that find the $K$-best
shortest paths in a graph.}}
@article{NaoBru-JCB-94,
title = {{On near-optimal alignments of biological sequences}},
author = {Dalit Naor and Douglas Brutlag},
journal = {J. Computational Biology},
volume = {1},
number = {4},
pages = {349--366},
year = {1994},
url = {http://cmgm.stanford.edu/~brutlag/Publications/naor94.html}}
@inproceedings{NguSchZha-HLTW-94,
title = {{Is $N$-best dead?}},
author = {L. Nguyen and Richard Schwartz and Y. Zhao and G. Zavaliagkos},
booktitle = {Proc. ARPA Human Language Technology Worksh.},
pages = {411--414},
year = {1994}}
@inproceedings{NicPit-ICT-96,
title = {{Towards network survivability by finding the $K$-best paths through
a trellis tree}},
author = {Stavros D. Nikolopoulos and Andreas Pitsillides},
booktitle = {Proc. Int. Conf. Telecommunications},
site = {Istanbul, Turkey},
pages = {817--821},
month = {April},
year = {1996}}
@inproceedings{NikPitTip-INFOCOM-97,
title = {{Addressing network survivability issues by finding the $K$-best
paths through a trellis graph}},
author = {Stavros D. Nikolopoulos and Andreas Pitsillides and David Tipper},
booktitle = {Proc. 16th Joint. Conf. IEEE Computer {\&} Communications Socs.},
volume = {1},
pages = {370--377},
month = {April},
year = {1997},
url = {ftp://violet.tele.pitt.edu/pub/Telecom_Faculty/Tipper/info97.ps},
abstract = {Due to the increasing reliance of society on the timely and
reliable transfer of large quantities of information (such as voice,
data, and video) across high speed communication networks, it is becoming
important for a network to offer survivability, or at least graceful
degradation, in the event of network failure. In this paper we aim to
offer a solution in the selection of the K-best disjoint paths through
a network by using graph theoretic techniques. The basic approach is
to map an arbitrary network graph into a trellis graph which allows the
application of computationally efficient methods to find disjoint paths.
Use of the knowledge of the K-best disjoint paths for improving the survivability
of ATM networks at the virtual path and virtual circuit level is discussed.}}
@inproceedings{NouHafGen-LCN-97,
title = {{A dynamic routing procedure for connections with quality of service
requirements}},
author = {M'hamed Nour and Abdelhakim Hafid and Michel Gendreau},
booktitle = {Proc. 22nd Conf. Local Computer Networks},
publisher = {IEEE},
pages = {460--468},
month = {November},
year = {1997},
annote = {The last paragraph of the intro seems more descriptive than the
actual abstract: ``In this paper, we present a routing procedure that
minimizes a cost function while satisfying the requested QoS. The cost
function could be defined in terms of QoS information, real money to
pay for the operation of network resources, number of hops between the
source and destination, network reliability, etc.; it is not restricted
to QoS information, such as the functions used in existing techniques
(e.g. minimizing the end-to-end delay). The routing procedure determines
a path that satisfies bandwidth, delay and loss rate requirements of
the connection to establish. This procedure limits its search space and
thus limits its response time as it uses a constrained modified Double-Sweep
Algorithm \cite{Shi-Nw-76} which finds the k-shortest path lengths between
a specified node and all other nodes in the graph. It also increases
the probability that the connection establishment will be successful
as it uses the most recent information on local resource availability.''}}
@inproceedings{NouMarAtw-INFORMS-98,
title = {{Simulation of network performance based connection admission
control}},
author = {M'hamed Nour and Ernesto de Queir{\'o}s Vieira Martins and J. William
Atwood and Michel Gendreau and Marta Margarida Braz Pascoal and Jos{\'e}
Lu{\'\i}s Esteves dos Santos},
booktitle = {INFORMS/CORS Montr{\'e}al '98},
year = {1998},
abstract = {ATM provides various classes and requires Connection Admission
Control procedures for deciding whether a new request from a user can
be accepted. The Objective of this presentation is to show how k-shortest
path algorithms may be used in the context of ATM Networks to provide
decisions for Connection Admission Control.}}
@inproceedings{NowTho-SCT-91,
title = {{An efficient implementation of the $N$-best algorithm for lexical
access (large vocabulary speech recognition)}},
author = {P. Nowell and H. S. Thompson},
booktitle = {Proc. 2nd Eur. Conf. Speech Communication and Technology},
volume = {2},
pages = {667--670},
year = {1991},
abstract = {The authors describe an efficient implementation of the $N$-best
algorithm for lexical access. An extension has been made to the original
algorithm which reduces the search space by 80{\%} whilst retaining over
99{\%} of the top ten optimal paths produced by the standard $N$-best algorithm.
The authors have also found that pruning can reduce the search space
further by a further 50{\%} without a significant loss of optimal paths.}}
@inproceedings{PasSanMar-INFORMS-98,
title = {{An algorithm for ranking loopless paths}},
author = {Marta Margarida Braz Pascoal and Jos{\'e} Lu{\'\i}s Esteves dos Santos
and Ernesto de Queir{\'o}s Vieira Martins},
booktitle = {INFORMS/CORS Montr{\'e}al '98},
year = {1998},
abstract = {A new algorithm is proposed for ranking paths as so as its
adaption for loopless paths. Comparative computational experiments are
also presented. This allows the ranking of more than half a million of
loopless paths in 10000 nodes, 100000 arcs euclidean networks in less
than half second.}}
@inproceedings{PasSanMar-OPTI-98,
title = {{Ranking paths and loopless paths}},
author = {Marta Margarida Braz Pascoal and Jos{\'e} Lu{\'\i}s Esteves dos Santos
and Ernesto de Queir{\'o}s Vieira Martins},
booktitle = {Proc. Optimization 98},
month = {July},
year = {1998}}
@phdthesis{Ped-PhD-68,
title = {{On directed communication networks}},
author = {Robert Dennis Pedersen},
school = {Southern Methodist Univ.},
year = {1968},
abstract = {Treats mathematically several aspects of directed communication
networks and presents results on optimum routing strategies in noisy
radio communication networks. In particular, techniques are presented
for the determination of all possible paths in directed networks. Solutions
to the $k^{\rm th}$ longest path problems are outlined, and a detailed
study of the implications of linear dependencies of network paths on
flow distributions is made. Also, relationships between link flows and
terminal flows imposed by linear dependencies of source node and sink
node combinations are derived and studied in detail. From this investigation
some interesting relationships between conventional cutset and incidence
matrices from linear graph theory are deduced.}}
@article{Per-Nw-86,
title = {{Implementation of algorithms for $K$ shortest loopless paths}},
author = {Aarni Perko},
journal = {Networks},
volume = {16},
pages = {149--160},
year = {1986},
review = {MR-87j-05102}}
@article{MR-87j-05102,
reviews = {Per-Nw-86},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Implementation of algorithms for $K$ shortest loopless paths}},
author = {Richard D. Ringeisen},
volume = {87j},
number = {05102},
year = {1987},
text = {In this paper, the authors implement various known algorithms for
doing the $k$ shortest path problem. Here, the problem is to obtain not
just the usual shortest path but also the collection of $k$ paths between
two given vertices which in total have the shortest lengths. They use
various implementation and data storage techniques to implement two well-known
algorithms due to S. Clarke et al. [J. Soc. Indust. Appl. Math. 11 (1963),
1096--1102; MR 28 {\#}3648] and J. Y. Yen [Management Sci. 17 (1970/71),
712--716; MR 45 {\#}9827] and to present a new algorithm which they refer
to as using ``loopless deviations''. After listing a general, rather generic
algorithm for the problem, the authors explain how to use tree relations
between paths to compare them. The original path is the root of a tree,
and deviations from a given path are the immediate successors in the
tree.
The paper includes a table which compares CPU times for the three algorithms
under various implementation techniques. It concludes with discussions
of storage requirements and of qualitative aspects of the problem.}}
@article{PerShi-JACM-78,
title = {{Finding two disjoint paths between two pairs of vertices in a
graph}},
author = {Yehoshua Perl and Yossi Shiloach},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {25},
number = {1},
pages = {1--9},
year = {1978}}
@article{Pie-Nw-75,
title = {{Bibliography on algorithms for shortest path, shortest spanning
tree, and related circuit routing problems (1956-1974)}},
author = {A. R. Pierce},
journal = {Networks},
volume = {5},
number = {2},
pages = {129--149},
month = {April},
year = {1975},
abstract = {This bibliography contains 431 references on algorithms and
machine calculation techniques for solving the shortest path, k-th shortest
path, and the shortest spanning tree problems. Chapter 1-Paths and Circuits-is
divided into four sections, dealing respectively with shortest path,
optimal path, Traveling Salesman and other related algorithms. Chapter
2 deals with spanning trees, and Chapter 3 covers the computer aided
design of electronic systems that utilize minimum path or shortest tree
algorithms.}}
@article{PieLas-MS-73,
title = {{Improved combinatorial programming algorithms for a class of
all-zero-one integer programming problems}},
author = {J. F. Pierce and J. S. Lasky},
journal = {Management Science},
volume = {19},
pages = {528--543},
year = {1973},
abstract = {In the present paper a number of improvements in earlier algorithms
are presented, including a new search strategy, methods for reducing
the original problem, and mechanisms for feasibility filtering in multi-word
problems. With these improvements problem-solving efficiency has been
increased in many instances by an order of magnitude. In addition, the
paper contains computational experience obtained in solving problems
for the k-best solutions.}}
@article{Pol-JMAA-61,
title = {{Solutions of the {$k$th} best route through a network---a review}},
author = {M. Pollack},
journal = {J. Math. Anal. and Appl.},
volume = {3},
pages = {547--559},
year = {1961}}
@article{Pol-OR-61,
title = {{The $k$th best route through a network}},
author = {M. Pollack},
journal = {Operations Research},
volume = {9},
pages = {578--580},
year = {1961}}
@inproceedings{Pol-ORSA-69,
title = {{Shortest path solutions of the the $k$th best route problems}},
author = {M. Pollack},
booktitle = {Proc. 36th Mtg. Operations Research Society of America},
journal = {Bull. Operations Research Soc. of America},
year = {1969}}
@article{PooLibSie-COR-99,
title = {{Solving the $k$-best traveling salesman problem}},
author = {Edo S. van der Poort and Marek Libura and Gerard Sierksma and
Jack A. A. van der Veen},
journal = {Computers and Operations Research},
volume = {26},
number = {4},
pages = {409--425},
month = {April},
year = {1999},
abstract = {Although k-best solutions for polynomial solvable problems
are extensively studied in the literature, not much is known for NP-hard
problems. In this paper we design algorithms for finding sets of k-best
solutions to the Traveling Salesman Problem (TSP) for some positive integer
k. It will be shown that a set of k-best Hamiltonian tours in a weighted
graph can be determined by applying the so-called partitioning algorithms
and by algorithms based on modifications of solution methods like branch-and-bound.
In order to study the effectiveness of these algorithms, the time for
determining a set of k-best solutions is investigated for a number of
instances in Reinelt's TSPLIB library. It appears that the time required
to find a set of k-best tours grows rather slowly in k. Furthermore,
the results of numerical experiments show that the difference in length
between a longest and a shortest tour in the set of k-best solutions
grows only slowly in k and that also the 'structure' of the tours in
the set of k-best tours is quite robust.}}
@article{RaiKum-IJE-86,
title = {{On path enumeration}},
author = {S. Rai and A. Kumar},
journal = {Int. J. Electronics},
volume = {60},
pages = {421--425},
year = {1986},
abstract = {The authors discuss a simple method for path enumeration in
reliability logic diagrams. The method utilizes only simple algebraic
concepts. It is straightforward and lacks computational complexity. An
example illustrates the method.}}
@article{RanBriSpe-CC-79,
title = {{Search for all self-avoiding paths for molecular graphs}},
author = {M. Randic and G. M. Brissey and R. B. Spencer and C. L. Wilkins},
journal = {Computers and Chemistry},
volume = {3},
number = {1},
pages = {5--13},
year = {1979},
abstract = {An algorithm which finds all paths through a molecular skeleton
(graph) is described. Programs implementing this algorithm in PL/1, BASIC
and FORTRAN are described and illustrative examples are shown. The number
of paths in a graph increases rapidly with the number of cycles, but
for most molecular graphs counting all paths is a practical task. Input
to the programs is the connectivity relationships for a molecule either
explicitly or in the form of adjacency matrix. As output, one may obtain
all paths (by listing of the atoms involved) or only the total number
of paths of each length. The latter is of interest for characterization
of structures, and is convenient in subsequent comparisons and searches
for structural similarities. It is suggested that the number of paths
in a graph be considered as a useful quantitative measure of the complexity
of a graph or structure.}}
@inproceedings{RaoDatRed-CUPUM-97,
title = {{Bus transit route generation by $K$-shortest path algorithm}},
author = {K. Ramachandra Rao and R. N. Datta and K. Sudhakara Reddy},
booktitle = {Proc. 5th Int. Conf. Computers in Urban Planning and Urban
Management},
publisher = {Indian Inst. of Technology, Bombay},
month = {December},
year = {1997}}
@article{RawBed-JFI-75,
title = {{On enumerating paths of $K$ arcs in unoriented complete graphs}},
author = {Eugene Rawdin and Samuel D. Bedrosian},
journal = {J. Franklin Inst.},
volume = {299},
number = {1},
pages = {73--76},
month = {January},
year = {1975},
abstract = {In an unoriented complete graph of $V$ vertices, let $K$ denote
the number of arcs in a path. Also, let $S(V,K)=$ number of paths of
$K$ arcs from one specified vertex to another; $SS(V,K)=$ number of paths
of $K$ arcs from one specified vertex to another. Theorems and tableaux
are given for $S(V,K)$ and $SS(V,K)$ as well as relations among the entries
in the tables. The final theorem indicates that for the the number of
paths of all possible lengths we have the remarkable approximation: $SS(V,K)\approx\epsilon
(V-2)!$.}}
@article{ReeTar-Nw-75,
title = {{Bounds on backtrack algorithms for listing cycles, paths, and
spanning trees}},
author = {R. C. Reed and Robert E. Tarjan},
journal = {Networks},
volume = {5},
number = {3},
pages = {237--252},
month = {July},
year = {1975},
abstract = {Backtrack algorithms for listing certain kinds of subgraphs
of a graph are described and analyzed. Included are algorithms for listing
all spanning trees, all cycles, all simple cycles, or all of certain
other kinds of paths. The algorithms have $O(V+E)$ space requirements
and $O(V+E+EN)$ time requirements, if the problem graph has $V$ vertices,
$E$ edges, and $N$ subgraphs of the type to be listed.}}
@article{Ren-EJOR-85,
title = {{Ranking scalar products to improve bounds for the quadratic assignment
problem}},
author = {F. Rendl},
journal = {Eur. J. Operational Research},
volume = {20},
pages = {363--372},
year = {1985},
abstract = {The eigenvalue bound for the quadratic assignment problem (QAP)
is successively improved by considering a set of k-best scalar products,
related to the QAP. An efficient procedure is proposed to find such a
set of k-best scalar products. A class of QAPs is described for which
this procedure in general improves existing lower bounds and at the same
time generates good suboptimal solutions. The method leaves the user
with a large flexibility in controlling the quality of the bound. However,
since the method is sensitive to input data it should only be used in
combination with other bounding rules.}}
@article{RibMinPen-EJOR-89,
title = {{An optimal column-generation-with-ranking algorithm for very
large-scale set partitioning problems in traffic assignment}},
author = {C. C. Ribeiro and M. Minoux and M. C. Penna},
journal = {Eur. J. Operational Research},
volume = {41},
number = {2},
pages = {232--239},
month = {July},
year = {1989}}
@inproceedings{RicOstRoh-ASSP-95,
title = {{Lattice-based search strategies for large vocabulary speech recognition}},
author = {F. Richardson and M. Ostendorf and J. R. Rohlicek},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {576--579},
month = {May},
year = {1995},
abstract = {The design of search algorithms is an important issue in large
vocabulary speech recognition, especially as more complex models are
developed for improving recognition accuracy. Multi-pass search strategies
have been used as a means of applying simple models early on to prune
the search space for subsequent passes using more expensive knowledge
sources. The pruned search space is typically represented by an $N$-best
sentence list or a word lattice. Here, we investigate three alternatives
for lattice search: $N$-best rescoring, a lattice dynamic programming
search algorithm and a lattice local search algorithm. Both the lattice
dynamic programming and lattice local search algorithms are shown to
achieve comparable performance to the $N$-best search algorithm while
running as much as 10 times faster on a 20k word lexicon; the local search
algorithm has the additional advantage of accommodating sentence-level
knowledge sources.}}
@article{RinRodSun-AML-00,
title = {{A simplification of the double-sweep algorithm to solve the $k$-shortest
path problem}},
author = {K. A. Rink and E. Y. Rodin and V. Sundarapandian},
journal = {Applied Math. Lett.},
volume = {13},
number = {8},
pages = {77--85},
month = {November},
year = {2000}}
@article{RinRodSun-MCP-99,
title = {{Routing airlift aircraft by the double-sweep algorithm}},
author = {K. A. Rink and E. Y. Rodin and V. Sundarapandian and M. A. Redfern},
journal = {Mathematical and Computer Modelling},
volume = {30},
number = {5--6},
pages = {133--147},
month = {September},
year = {1999},
abstract = {We describe the problem of modeling the routing of aircraft
across a network of enroute bases. This is done to provide routes for
scenarios that are being studied by the analysis tools at the Airlift
Mobility Command (AMC). We are primarily concerned with the development
of routes that can be easily implemented with the airlift operations
analysis tools in use at AMC. We describe the specific implementation
issues that have been addressed. One such issue is the use of available
data in a specific input file format. Another crucial issue is adapting
the base-to-base route set provided by the double-sweep algorithm into
a region-to-region route set which can be used by the airlift analysis
models. The methods used to adapt the route sets appropriately are described,
and test results are provided for two different scenarios. Finally, recommendations
that were given to the analysts at AMC for use of the k-shortest path
routine are given.}}
@techreport{Rom-TR-93,
title = {{On enumeration of near to best solutions in discrete and dynamic
programming}},
author = {J. V. Romanovsky},
institution = {DIMACS},
number = {93-64},
year = {1993},
url = {http://dimacs.rutgers.edu/techps/1993/93-64.ps},
abstract = {We consider a new approach to enumeration of near-to-optimal
solutions in discrete optimization problems. The main idea is to consider
the processes that generate such solutions, and to describe possible
operations with the processes. The preliminary set of operations is proposed
in the paper. This set allows ones to construct a rather standard tool
for enumeration in those optimization problems that may be solved with
ideas of splitting (as in Branch-and-Bound) and recursion (as in Dynamic
programming). As examples we considered the problems of shortest and
the quickest paths in a graph, and the non-serial dynamic programming.
Some experimenal software were developed to check the ideas. It was described
at the end of the paper.}}
@article{RosSunXue-COR-91,
title = {{Algorithms for the quickest path problem and the enumeration
of quickest paths}},
author = {J. B. Rosen and S.-Z. Sun and G.-L. Xue},
journal = {Computers and Operations Research},
volume = {18},
pages = {579--584},
year = {1991},
abstract = {Let $N=(V,A,c,l)$ be an input network with node set $V$, arc
set $A$, positive arc weight function $c$ and nonnegative arc weight
function l. Let sigma be the amount of data to be transmitted. The quickest
path problem is to find a routing path in $N$ to transmit the given amount
of data in minimum time. Y. L. Chen and Y. H. Chin (1990) proposed this
problem and developed algorithms for the single pair quickest path problem
with time complexity $O(re+rn\log{n})$, where $n=|V|$, $e=|A|$, and $r$
is the number of distinct capacity values of $N$. The authors develop
an alternative algorithm for the single pair quickest path problem with
same time complexity and less space requirement. They then study the
constrained quickest path problem and propose an $O(re+rn\log{n})$ time
algorithm. Finally, they develop an algorithm to enumerate the first
$m$ quickest paths to send a given amount of data from one node to another
with time complexity $O(rmne+rmn^2\log{n})$.}}
@article{RoyGal-RAIRO-73,
title = {{Enumeration of $\epsilon$-minimum admissible paths between two
points}},
author = {B. Roy and D. Galland},
journal = {Revue Francaise d'Automatique Informatique Recherche Operationelle
(RAIRO)},
volume = {7},
number = {V3},
pages = {3--20},
month = {September},
year = {1973},
abstract = {Let $G=(X,U)$ be a network to every arc of which corresponds
a length $a(u)\in R$. A path $\mu$ joining two nodes $x_1$ and $x_n$
is said $\epsilon$-minimum if its length $a(\mu)$ is at most $\epsilon$
bigger than the length of the shortest path of $G$ joining $x_1$ to $x_n$.
This path will be admissible if it also satisfies to some constraints
concerning the succession of arcs and nodes of which it is composed.
This paper describes an algorithm allowing the enumeration of all $\epsilon$-minimum
admissible paths joining $x_1$ to $x_n$ for a rather general set of admissibility
constraints. It is based upon a Procedure of Separation and Evaluation
in Sequence. The paper gives a practical examples and some precisions
on a program written for C.D.C. 6600 and its performances.}}
@article{Rub-IEICE-78,
title = {{Enumerating all simple paths in a graph}},
author = {F. Rubin},
journal = {IEICE Trans. Circuits {\&} Systems},
volume = {CAS-25},
number = {8},
pages = {641--642},
month = {August},
year = {1978},
abstract = {Warshall's theorem is used to obtain a matrix power algorithm
for enumerating all simple paths in a graph. The algorithm uses $O(N^3)$
matrix operations, compared to $O(N^4)$ operations for previous algorithms.}}
@article{Rup-Algo-00,
title = {{Finding the $k$ shortest paths in parallel}},
author = {Eric Ruppert},
journal = {Algorithmica},
volume = {28},
number = {2},
pages = {242--254},
month = {October},
year = {2000}}
@mastersthesis{Rup-MS-96,
title = {{Parallel algorithms for the $k$ shortest paths and related problems}},
author = {Eric Ruppert},
school = {Univ. of Toronto, Dept. of Computer Science},
year = {1996},
url = {http://www.cs.utoronto.ca/~ruppert/thesis.ps.gz}}
@inproceedings{Rup-STACS-97,
title = {{Finding the $k$ shortest paths in parallel}},
author = {Eric Ruppert},
booktitle = {Proc. 14th Symp. Theoretical Aspects of Computer Science},
month = {February},
year = {1997},
note = {A concurrent-read exclusive-write PRAM algorithm is developed to
find the $k$ shortest paths between pairs of vertices in an edge-weighted
directed graph. Repetitions of vertices along the paths are allowed.
The algorithm computes an implicit representation of the $k$ shortest
paths to a given destination vertex from every vertex of a graph with
$n$ vertices and $m$ edges, using $O(m + nk\log^2 k)$ work and $O(\log^3
k\log^* k + \log n(\log\log k + \log^* n))$ time, assuming that a shortest
path tree rooted at the destination is precomputed. The paths themselves
can be extracted from the implicit representation in $O(\log L\log n)$
time, and $O(n\og n + L)$ work, where $L$ is the total length of the
output.}}
@article{SaiOikOno-IEICE-80,
title = {{Generation of all trees and the hybrid system to check the graph
connectivities}},
author = {K. Saisyu and H. Oikawa and R. Onodera and Y. Taniguchi},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E63},
number = {1},
pages = {78--79},
month = {January},
year = {1980},
abstract = {Describes a system to check graph connectivities and some procedures
for generating all subgraphs of a linear graph without duplication using
it. The sets of trees, circuits, paths and simple cutsets can be listed
with this method. The system is composed of link circuits, node circuits
and control circuits. The link and node circuits correspond to links
and nodes of a graph respectively. The system is controlled by a microcomputer.
To list a set of subgraph, the terminals of link circuits and nodes circuits
are connected according to the graph and the computer controls the system
to make subgraphs and lists the set. The system is simple in construction
and since operation is very fast the procedure becomes more efficient
than other well-known methods.}}
@techreport{Sak-TR-66,
title = {{The $k$ shortest routes and the $k$ shortest chains in a graph}},
author = {M. Sakarovitch},
institution = {Univ. of California, Berkeley, Operations Research Ctr.},
number = {ORC 66-32},
year = {1966}}
@inproceedings{SanMar-INFORMS-98,
title = {{Ranking paths in the multiobjective shortest path problem}},
author = {Jos{\'e} Lu{\'\i}s Esteves dos Santos and Ernesto de Queir{\'o}s Vieira Martins},
booktitle = {INFORMS/CORS Montr{\'e}al '98},
year = {1998},
abstract = {A new algorithm is proposed for the biobjective shortest path
problem, which is based on the ranking of shortest paths. The inportance
of the ojective function in the ranking problem is shown and comparative
computational experiments are presented.}}
@inproceedings{SanPasMar-OPTI-98,
title = {{A new algorithm for the multiobjective shortest path problem}},
author = {Jos{\'e} Lu{\'\i}s Esteves dos Santos and Marta Margarida Braz Pascoal
and Ernesto de Queir{\'o}s Vieira Martins},
booktitle = {Proc. Optimization 98},
month = {July},
year = {1998}}
@article{SaqBatSte-PE-92,
title = {{Towards an automatic method of predicting protein structure by
homology: an evaluation of suboptimal sequence alignments}},
author = {M. A. S. Saqi and P. Bates and M. J. E. Sternberg},
journal = {Protein Engineering},
volume = {5},
number = {4},
pages = {305--311},
month = {June},
year = {1992},
abstract = {A major problem in predicting protein structure by homology
modelling is that the sequence alignment from which the model is built
may not be the best one in terms of the correct equivalencing of residues
assessed by structural or functional criteria. A useful strategy is to
generate and examine a number of suboptimal alignments as better alignments
can often be found away from the optimal. A procedure to filter rapidly
suboptimal alignments based on measurement of core volumes and packing
pair potentials is investigated. The approach is benchmarked on three
pairs of sequences which are non-trivial to align correctly, namely two
immunoglobulin domains, plastocyanin with azurin and two distant globin
sequences. It is shown to be useful to reduce a large ensemble of possible
alignments down to a few which correspond more closely to the correct
(structure based) alignment.}}
@article{SaqSte-JMB-91,
title = {{A simple method to generate non-trivial alternative alignments
of protein sequences}},
author = {M. A. S. Saqi and M. J. E. Sternberg},
journal = {J. Mol. Biol.},
volume = {219},
number = {4},
pages = {727--732},
month = {June},
year = {1991},
abstract = {A major problem in sequence alignments based on the standard
dynamic programming method is that the optimal path does not necessarily
yield the best equivalencing of residues assessed by structural or functional
criteria. An algorithm is presented that finds suboptimal alignments
of protein sequences by a simple modification to the standard dynamic
programming method. The standard pairwise weight matrix elements are
modified in order to penalize, but not eliminate, the equivalencing of
residues obtained from previous alignments. The algorithm thereby yields
a limited set of alternate alignments that can differ considerably from
the optimal. The approach is benchmarked on the alignments of immunoglobulin
domains. Without a prior knowledge of the optimal choice of gap penalty,
one of the suboptimal alignments is shown to be more accurate than the
optimal.}}
@article{SarMat-SJO-93,
title = {{A note on $K$-best solutions to the Chinese postman problem}},
author = {Yasufumi Saruwatari and Tomomi Matsui},
journal = {SIAM J. Optimization},
publisher = {SIAM},
volume = {3},
number = {4},
pages = {726--733},
year = {1993},
review = {MR-95a-90087}}
@article{MR-95a-90087,
reviews = {SarMat-SJO-93},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A note on $K$-best solutions to the Chinese postman problem}},
author = {Svatopluk Poljak},
volume = {95a},
number = {90087},
year = {1995},
text = {The authors present a polynomial time algorithm to find $K$-best
solutions to the Chinese postman problem (CPP). The time complexity of
their algorithm is $$O(S(n,m) + K(n + m + \log K + nT(n+m,m)))$$ where
$S(s,t)$ is the complexity of the ordinary Chinese postman problem and
$T(s,t)$ is the complexity of a post-optimal algorithm for nonbipartite
matching in a graph with $s$ vertices and $t$ edges. The authors first
analyze the properties of the 2-best solution to the CPP. $K$-best solutions
are then found by solving 2-best CPP iteratively.}}
@inproceedings{Sch-CA-94,
title = {{Vector-weighted matchings}},
author = {Dietmar Schweigert},
booktitle = {Combinatorics Advances},
number = {329},
series = {Math. Appl.},
publisher = {Kluwer},
pages = {267--276},
year = {1994},
review = {MR-96k-90059}}
@article{MR-96k-90059,
reviews = {Sch-CA-94},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Vector-weighted matchings}},
author = {Peter Butkovic},
volume = {96k},
number = {90059},
year = {1996},
text = {Consider a complete bipartite graph $G$ the edges of which are
weighted by nonnegative real vectors. The weight of a matching $M$ in
$G$ (notation $w(M)$) is the sum of the weights of edges in $M$. A perfect
matching $M$ in $G$ is called an efficient solution if there is no perfect
matching $M'$ in $G$ such that $w(M)\leq w(M')$ with strict inequality
in at least one component. The task is to find all efficient solutions
in $G$. It is shown that the method of preference functions finds some
but in general not all efficient solutions. Another method called ``descent
on a chain'' based on a repeated use of an algorithm for finding the $K$-best
solutions to the classical assignment problem is proposed but an example
indicates that it is computationally very hard.}}
@article{Sch-SJC-98,
title = {{All highest scoring paths in weighted grid graphs and their application
to finding all approximate repeats in strings}},
author = {Jeannette P. Schmidt},
journal = {SIAM J. Computing},
publisher = {SIAM},
volume = {27},
number = {4},
pages = {972--992},
month = {August},
year = {1998},
abstract = {Weighted paths in directed grid graphs of dimension $(m\times
n)$ can be used to model the string edit problem, which consists of obtaining
optimal (weighted) alignments between substrings of $A$, $|A|=m$, and
substrings of $B$, $|B|=n$. We build a data structure (in $O(mn\log m)$
time) that supports $O(\log m)$ time queries about the weight of any
of the $O(m^2n)$ best paths from the vertices in column 0 of the graph
to all other vertices. Using these techniques we present a simple $O(n^2\log
n)$ time and $\Theta(n^2)$ space algorithm to find all (the locally optimal)
approximate tandem (or nontandem) repeats $xy$ within a string of size
$n$. This improves (by a factor of $\log n$) upon several previous algorithms
for this problem and is the first algorithm to find {\em all locally
optimal} repeats. For edit graphs with weights in $\{0,-1,1\}$, a slight
modification of our techniques yields an $O(n^2)$ algorithm for the cyclic
string comparison problem, as compared to $O(n^2\log n)$ for the case
of general weights.}}
@article{Sha-JIE-80,
title = {{Path finding algorithm --- an algebraic method}},
author = {J. K. R. Shastry},
journal = {J. Inst. of Engineers (India) Electronics {\&} Telecommunication
Engineering Div.},
volume = {60},
number = {ET-3},
pages = {76--78},
month = {April},
year = {1980},
abstract = {An efficient algorithm for determining all paths between a
terminal node pair of a non-oriented network has been proposed. The algorithm
is suitable both for hand computation and, when the network is large,
for programming on a digital computer. The memory requirement in this
method is much less than in other existing methods.}}
@inproceedings{ShaSmi-INPS-83,
title = {{The reliability of a computer communication network under a given
level of traffic}},
author = {F. Shatwan and D. G. Smith},
booktitle = {Proc. 2nd Int. Network Planning Symp., Networks 83},
pages = {310--315},
year = {1983},
abstract = {In probabilistic reliability analysis the network is represented
by a graph. The nodes correspond to computer centres and the edges correspond
to links between the centres. Each element (link or node) is given a
probability of being operative. The usual aim is to find either the terminal
reliability, which is the probability that at least one path exists between
a given pair of nodes, or global reliability, which is the probability
that at least one path exists between every pair of nodes. Four methods
are suggested to determine terminal reliability and unreliability. In
methods one and three, path enumeration is used to determine terminal
reliability, and in methods two and four terminal unreliability is found
by using cutset enumeration. Monte Carlo techniques are also used in
methods three and four.}}
@article{She-MR-95,
title = {{A new simple algorithm for enumerating all minimal paths and
cuts of a graph}},
author = {Yuanlong Shen},
journal = {Microelectronics and Reliability},
volume = {35},
number = {6},
pages = {973--976},
month = {June},
year = {1995},
abstract = {There are many algorithms to enumerate MPS and MCS. All of
these involve advanced mathematics. This paper presents a new simple
algorithm to determine all minimal paths between specified single terminal
pair of arbitrary graphs or to determine all minimal cuts when the graph
is planar. The algorithm is based on elementary concept of graph theory
and dual principle. This algorithm is fast and simple. An example illustrates
the algorithm.}}
@mastersthesis{Shi-BS-95,
title = {{Finding the $k$ shortest paths by AI search techniques}},
author = {Tetsuo Shibuya},
type = {Bachelors Thesis},
school = {Univ. of Tokyo, Faculty of Science},
year = {1995}}
@article{Shi-ISM-95,
title = {{Finding the $k$ shortest paths by AI search techniques}},
author = {Tetsuo Shibuya},
journal = {Cooperative Research Reports in Modeling and Algorithms},
publisher = {Inst. of Statical Mathematics},
address = {Tokyo},
volume = {7},
number = {77},
pages = {212--222},
month = {March},
year = {1995}}
@inproceedings{Shi-JNM-76,
title = {{Algorithms for finding the $k$ shortest paths in a network}},
author = {Douglas R. Shier},
booktitle = {ORSA/TIMS Joint National Mtg.},
journal = {Bull. Operations Research Soc. of America},
pages = {115},
year = {1976},
abstract = {It is sometimes important to find not only paths of minimum
length in a network but also paths that have nearly minimum length. Several
algorithms for computing these k shortest paths are presented, and computational
experience with such algorithms on networks having several hundred nodes
is described. The relative strengths and weaknesses of these algorithms
for certain types of network structures are also discussed.}}
@mastersthesis{Shi-MS-97,
title = {{New Approaches to Flexible Alignment of Multiple Biological Sequences}},
author = {Tetsuo Shibuya},
address = {Faculty of Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, JAPAN},
school = {Univ. of Tokyo, Dept. of Information Science},
month = {February},
year = {1997},
url = {http://naomi.is.s.u-tokyo.ac.jp/papers/THESIS/MASTER/shibuya.ps.gz}}
@article{Shi-NBS-74,
title = {{Computational experience with an algorithm for finding the $K$
shortest paths in a network}},
author = {Douglas R. Shier},
journal = {J. Res. Nat. Bur. Standards Sec. B},
volume = {78B},
pages = {139--165},
year = {1974},
review = {MR-50-12195}}
@article{MR-50-12195,
reviews = {Shi-NBS-74},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Computational experience with an algorithm for finding the $K$
shortest paths in a network}},
volume = {50},
number = {12195},
year = {1975}}
@article{Shi-Nw-76,
title = {{Iterative methods for determining the $k$ shortest paths in a
network}},
author = {Douglas R. Shier},
journal = {Networks},
volume = {6},
number = {3},
pages = {205--229},
year = {1976},
abstract = {Presents and develops an algebraic structure for determining
the k shortest paths from a given node to all other nodes of a network.
Three new methods for calculating such k shortest path information are
examined and compared. These methods are based on a fairly strong analogy
which exists between the solution of such network problems and traditional
techniques for solving linear equations. On the basis of both theoretical
and computational evidence, one of the three methods is seen to offer
an extremely effective procedure for finding the k shortest paths from
a given node in a network.},
review = {MR-56-2294}}
@article{MR-56-2294,
reviews = {Shi-Nw-76},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Iterative methods for determining the $k$ shortest paths in a
network}},
author = {M. M. Sys{\l}o},
volume = {56},
number = {2294},
year = {1978}}
@article{Shi-Nw-79,
title = {{On algorithms for finding the $k$ shortest paths in a network}},
author = {Douglas R. Shier},
journal = {Networks},
volume = {9},
number = {3},
pages = {195--214},
year = {1979},
review = {MR-80g-90047}}
@article{MR-80g-90047,
reviews = {Shi-Nw-79},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On algorithms for finding the $k$ shortest paths in a network}},
volume = {80g},
number = {90047},
year = {1980},
text = {This paper presents, within a unified framework, several new algorithms
for computing $k$ shortest paths in a network. These algorithms utilize
strategies which have proved to be efficient in solving shortest path
problems. In addition, a computational study was conducted to assess
the effects of the different `arc processing' orders which are characteristic
of each algorithm. Testing was performed using generated classes of moderately
large grid, complete and random networks. Two particular algorithms emerge
as the most promising among those evaluated.}}
@inproceedings{ShiIkeIma-ITS-95,
title = {{Finding a realistic detour by AI search techniques}},
author = {Tetsuo Shibuya and T. Ikeda and Hiroshi Imai and Shigeki Nishimura
and Hiroshi Shimoura and Kenji Tenmoku},
booktitle = {Proc. 2nd Intelligent Transportation Systems},
volume = {4},
pages = {2037--2044},
month = {November},
year = {1995},
url = {http://naomi.is.s.u-tokyo.ac.jp/papers/navigation/suboptimal-routes/ITS95/its.ps.gz}}
@inproceedings{ShiIma-GIW-93,
title = {{Finding $K$-best alignments of multiple sequences}},
author = {G. Shibayama and Hiroshi Imai},
booktitle = {Proc. Genome Informatics Worksh. IV},
publisher = {Universal Academy Press},
pages = {120--129},
year = {1993},
url = {http://naomi.is.s.u-tokyo.ac.jp/papers/genome/suboptimal.ps.gz},
abstract = {Detecting similarities of multiple genome sequences is one
of the most important topics in genome informatics. For the purpose of
finding such similarities, an alignment with the highest score with respect
to some similarity criterion is provided as an output. However, the alignment
with the best score is not necessarily the most significant alignment
of the sequences from the viewpoint of biology. In this respect, providing
suboptimal alignments is very useful. Since finding an alignment of sequences
corresponds to finding a path in some directed acyclic graph, we propose
a simple algorithm to enumerate all $K$-best alignments in order, where
$K$ may not necessarily be specified beforehand, by finding the $K$ longest
paths in the graph. We further consider finding the subgraph formed by
such $K$ longest paths. Several useful approaches to find the optimal
paths in a graph are also mentioned.}}
@article{ShiIma-IPSJ-96,
title = {{Suboptimal alignments of multiple biological sequences}},
author = {Tetsuo Shibuya and Hiroshi Imai},
journal = {IPSJ SIG Notes},
volume = {SIGAL51-1},
pages = {1--8},
month = {May},
year = {1996}}
@inproceedings{ShiIma-ISMB-96,
title = {{Suboptimal alignments of multiple biological sequences}},
author = {Tetsuo Shibuya and Hiroshi Imai},
booktitle = {Intelligent Systems in Molecular Biology},
pages = {76},
month = {June},
year = {1996},
note = {Poster session abstract.}}
@inproceedings{ShiIma-PSB-97,
title = {{Enumerating suboptimal alignments of multiple biological sequences
efficiently}},
author = {Tetsuo Shibuya and Hiroshi Imai},
booktitle = {Proc. 2nd Pacific Symp. Biocomputing},
pages = {409--420},
month = {January},
year = {1997},
url = {http://www-smi.stanford.edu/people/altman/psb97/shibuya.pdf}}
@inproceedings{ShiIma-RECOMB-97,
title = {{New flexible approaches for multiple sequence alignment}},
author = {Tetsuo Shibuya and Hiroshi Imai},
booktitle = {Proc. 1st Int. Conf. Computational Molecular Biology},
publisher = {ACM},
pages = {267--276},
month = {January},
year = {1997},
url = {http://naomi.is.s.u-tokyo.ac.jp/papers/genome/recomb97.ps.gz}}
@inproceedings{ShiImaNis-CODAS-96,
title = {{Detour queries in geographical databases for navigation and related
algorithm animations}},
author = {Tetsuo Shibuya and Hiroshi Imai and Shigeki Nishimura and Hiroshi
Shimoura and Kenji Tenmoku},
booktitle = {Proc. Int. Symp. Cooperative Database Systems for Advanced
Applications},
volume = {2},
pages = {333--340},
month = {December},
year = {1996},
url = {http://naomi.is.s.u-tokyo.ac.jp/papers/databases/codas96.ps.gz}}
@article{ShiIshIto-JJFTS-98,
title = {{Shortest path problems in fuzzy network}},
author = {F. Shimada and H. Ishii and T. Itoh},
journal = {Japanese J. Fuzzy Th. and Systems},
volume = {10},
number = {2},
pages = {221--232},
year = {1998},
abstract = {We extend traditional shortest path models to fuzzy versions
with the existence possibility of arcs and fuzzy arc length. First,
we consider the model where existence of each arc is fuzzy but its length
is ordinary number. That is, we maximize the possibility of the existence
of the path and minimize the length of the path, and seek nondominated
paths since usually there does not exist a path that optimizes both criteria
at a time. In order to solve this problem, we first find an optimal path
on an ordinary network with arcs whose existence possibility is maximum
by the Floyd-Warshall method. Next, repeatedly arcs with lower existence
possibilities are added to the network and nondominated paths are found.
Further, we extend this solution procedure to the shortest path problem
whose arc lengths are fuzzy numbers.}}
@article{ShiTsuShi-IEICE-87,
title = {{On a second shortest $k$-tuple of edge-disjoint paths}},
author = {S. Shinoda and S. Tsukiyama and I. Shirakawa},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E70},
number = {10},
pages = {945--950},
month = {October},
year = {1987},
abstract = {Let $G$ be a directed graph containing $n$ nodes and $m$ edges,
with each edge of non-negative length. Given two specified nodes $s$
and $t$, the length of a $k$-tuple of edge-disjoint paths from $s$ to
$t$ in $G$ is the sum of the lengths of all the edges on these $k$ paths.
A polynomial time algorithm for finding a shortest $k$-tuple of edge-disjoint
paths from $s$ to $t$ in $G$ has been devised. Based on this algorithm,
the authors consider the problem of finding a second shortest $k$-tuple
of edge-disjoint paths from $s$ to $t$ in $G$, for which an $O(\min(n^3,nm\log
n))$-time algorithm is described.}}
@inproceedings{ShiYou-ICSLP-94,
title = {{Computer assisted grammar construction}},
author = {H.-H. Shih and S. J. Young},
booktitle = {Proc. Int. Conf. Spoken Language Processing},
publisher = {Acoustical Soc. Japan},
volume = {2},
pages = {855--858},
month = {September},
year = {1994},
abstract = {The paper presents a system for computer assisted grammar construction
(CAGC) and its application in speech processing. The CAGC system is designed
to infer linguistically-motivated broad-coverage stochastic context-free
grammars (SCFGs) for large corpora, without requiring significant manual
contributions. Our approach utilizes an extended inside-outside learning
algorithm to train a hybrid SCFG from a bracketed training set. The bracketing
information is derived by an automatic surface bracketing system (AUTO)
specifically designed for this purpose. Experimental results, evaluated
by using Parseval metrics, demonstrate that the CAGC system is capable
of inferring a grammar from a subset of the Wall Street Journal (WSJ)
tagged text corpus and that the inferred grammar achieves high coverage
and good precision. As an application, the inferred grammar acts as a
language model for rescoring $N$-best outputs from a speech recognizer.}}
@inproceedings{Sin-ICT-98,
title = {{Minimum cost routing and wavelength allocation using a genetic-algorithm/heuristic
hybrid approach}},
author = {Mark C. Sinclair},
booktitle = {Proc. 6th IEE Conf. Telecommunications},
month = {March},
year = {1998},
url = {http://esewww.essex.ac.uk/~mcs/ict98_sin.html},
annote = {Describes early results in minimum cost routing and wavelength
allocation of multi-wavelength all-optical transport networks using a
genetic-algorithm/heuristic hybrid approach in which path mutation simply
selects a path at random from the k-shortest paths.}}
@inproceedings{Sin-RION-92,
title = {{Single-moment analysis of unreliable trunk networks employing
$K$-shortest-path routing}},
author = {Mark C. Sinclair},
booktitle = {Proc. IEE Colloq. Resilience in Optical Networks},
pages = {3/1--6},
month = {October},
year = {1992},
url = {http://esewww.essex.ac.uk/~mcs/ps/RION_sin.ps.gz},
abstract = {In a recent paper, two methods were given for the single-moment
analysis of fixed-alternative-routing (FAR) circuit-switched communications
networks with reliable nodes but unreliable links. The second of these,
MKV_GOS, employs a Markov model for an unreliable link, in combination
with earlier work, so as to greatly reduce execution time compared to
existing algorithms.
In the current paper, an extension to the MKV_GOS method, which was originally
limited to OOC-SF (Originating Office Control with Spill-Forward) table-based
routing, is described. This extension allows the analysis of networks
employing two additional types of routing, K-shortest-disjoint-loopless-path
and K-shortest-loopless-path. The extended method is then demonstrated
by comparing results for the two K-shortest-path routing types in terms
of their overall NGOS for an example network. In addition, the execution
time of the method for a series of networks of increasing size is presented.}}
@incollection{SkiGol-AOR-89,
title = {{Solving $k$-shortest and constrained shortest path problems efficiently}},
author = {Christopher C. Skicism and Bruce Leonard Golden},
booktitle = {Network Optimization and Applications},
number = {20},
editor = {Bala Shetty},
series = {Annals of Operations Research},
publisher = {Baltzer Science Publishers},
pages = {249--282},
year = {1989},
review = {MR-90i-90048}}
@article{MR-90i-90048,
reviews = {SkiGol-AOR-89},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Solving $k$-shortest and constrained shortest path problems efficiently}},
volume = {90i},
number = {90048},
year = {1990},
text = {In this paper, we examine the problems of finding the $k$-shortest
paths, the $k$-shortest paths without repeated nodes, and the shortest
path with a single side constraint between an origin and destination
pair. Distances are assumed to be nonnegative, but networks may be either
directed or undirected. Two versions of algorithms for all these problems
are compared. The computational results show that, in each case, the
advantage of the adaptive version (as measured by total number of permanent
labels) grows with the problem size.}}
@article{SkiGol-Nw-87,
title = {{Computing $k$-shortest path lengths in Euclidean networks}},
author = {Christopher C. Skicism and Bruce Leonard Golden},
journal = {Networks},
volume = {17},
number = {3},
pages = {341--352},
year = {1987},
review = {MR-88k-90068}}
@article{MR-88k-90068,
reviews = {SkiGol-Nw-87},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Computing $k$-shortest path lengths in Euclidean networks}},
volume = {88k},
number = {90068},
year = {1988},
text = {In this paper, we examine the problem of finding $k$-shortest paths
between an origin and destination pair when distances are Euclidean.
Two versions of a generalized Dijkstra algorithm are compared. Computational
results show that the advantage of the adaptive version (measured by
total number of permanent labels) grows with both $k$ and the network
size. For large networks, the adaptive algorithm exhibits a 100:1 advantage
in the number of permanent labels set.}}
@article{Slo-BSTJ-72,
title = {{On finding the paths through a network}},
author = {Neil J. A. Sloane},
journal = {Bell System Technical J.},
volume = {51},
number = {2},
pages = {371--390},
month = {February},
year = {1972},
abstract = {Given a directed graph $G$, algorithms are discussed for finding
all paths through $G$ with prescribed originating and terminating nodes,
a subset of these paths containing all the edges, a subset containing
all the edge-edge transitions, and a subset containing the most likely
paths.}}
@inproceedings{Smi-SCS-88,
title = {{Routing in evacuation networks with Q-GERT and QNET-C}},
author = {J. MacGregor Smith},
booktitle = {Proc. 5th SCS Simulators Conf.},
pages = {311--315},
year = {1988},
abstract = {The optimal routing of occupants in emergency situations is
a difficult transient, integer, nonlinear programming problem. A design
methodology is presented for routing occupants based on a multiobjective
K-shortest path routing algorithm. The design methodology can be incorporated
into any simulation or analytical model for calculating an egress network's
performance measures and routing the occupants. Along with a description
of the problem, design methodology, and routing algorithm, computational
experience with the design methodology is also presented.}}
@article{SolGorSou-TRB-98,
title = {{Using decomposition in large-scale highway network design with
a quasi-optimization heuristic}},
author = {R. S. Solanki and J. K. Gorti and F. Southworth},
journal = {Transportation Research, Part B. -- Methodological},
volume = {32B},
number = {2},
pages = {127--140},
month = {February},
year = {1998},
abstract = {The highway network design problem deals with the selection
of links from a base network to facilitate the flow of vehicles from
origins to destinations. A proper selection of links requires a balance
between minimization of travel costs from origins to destinations and
minimization of costs incurred in building or improving links in the
network. Link construction costs are usually minimized as a part of the
objective or constrained by budget availability. National or regional
highway network design problems require excessive amounts of computing
time, if solved to optimality. This paper presents a variation of the
modified quasi-optimization (MQO) heuristic developed by Dionne and Florian
(1979). The proposed algorithm solves a large network design problem
by decomposing it in a sequence of smaller problems. Additional savings
in computation time are achieved by limiting the search in the MQO heuristic
to a well-designed set of paths for each OD pair. These paths are generated
to suit the network design problem and differ from the K-shortest paths
for the OD pairs. The combined use of decomposition and a limited set
of paths allows the proposed heuristic to address realistic network design
problems. Numerical experience with a problem involving 6563 nodes and
9800 two-ways links is reported.}}
@article{Son-C-79,
title = {{An algorithm for searching alternative routes in traffic networks}},
author = {H. Sonntag},
journal = {Computing},
volume = {21},
number = {4},
pages = {323--331},
year = {1979},
abstract = {A tree building algorithm which calculates all relevant alternative
routes in traffic networks is represented. Routes are called relevant,
when they progress steadily from the origin. The efficiency of the algorithm
with regard to the computer time compared to existing $k$ shortest paths
algorithms is remarkable.}}
@inproceedings{Str-ICSLP-94,
title = {{Experiments with a new algorithm for fast speaker adaptation}},
author = {N. Strom},
booktitle = {Proc. Int. Conf. Spoken Language Processing},
publisher = {Acoustical Soc. Japan},
volume = {2},
pages = {459--462},
month = {September},
year = {1994},
abstract = {A new method for improving continuous speech recognition (CSR)
using speaker adaptation is introduced. The proposed method is unsupervised-no
prior information about the speaker is used and there is no training
phase involved. The effect of speaker adaptation is achieved by assuming
that a set of speaker parameters is constant over the utterance. Both
the acoustic information and the speaker parameters condition the phoneme
classification. This approach makes it possible to search for the optimal
speaker parameters and the optimal phoneme sequence in a unified optimisation
procedure. The general method is tested using speech recognition based
on a segmental artificial neural network (ANN). The results from this
first test are reported. The performance on the utterance level, measured
as the position of the correct phoneme string in the sorted list of highest
scoring hypotheses ($N$-best list) is improved even for very short utterances.
The contribution to phoneme classification performance is positive only
when recognising long utterances.}}
@mastersthesis{Sub-MS-97,
title = {{Routing algorithms for dynamic, intelligent transportation networks}},
author = {Shivaram Subramanian},
school = {Virginia Technical Univ., Dept. of Civil Engineering},
month = {September},
year = {1997},
url = {http://scholar.lib.vt.edu/theses/public/etd-9797-123411/etd-title.html},
abstract = {Traffic congestion has been cited as the most conspicuous problem
in traffic management. It has far-reaching economic,social and political
effects. Intelligent Transportation Systems (ITS) research and development
programs have been assigned the task of developing sophisticated techniques
and counter-measures to reduce traffic congestion to manageable levels,
and also achieve these objectives using area-wide traffic management
methods. During times of traffic congestion, the traffic network in a
transient, time-dynamic state, and resembles a dynamic network. In addition,
in the context of ITS, the network can accurately detect such transient
behavior using traffic sensors, and several other information gathering
devices. In conjunction with Operations Research techniques, the time-varying
traffic flows can be routed through the network in an optimal manner,
based on the feedback from these information sources. Dynamic Traffic
Assignment (DTA) methods have been proposed to perform this task. An
important step in DTA is the calculation of user-optimal, system-optimal,
and multiple optimal routes for assigning traffic. One would also require
the calculation of user-optimal paths for vehicle scheduling and dispatching
problems.
The main objective of this research study is to analyze the effectiveness
of time-dependent shortest path (TDSP) algorithms and k-shortest path
(k-SP) algorithms as a practical routing tool in such intelligent transportation
networks. Similar algorithms have been used to solve routing problems
in computer networks. The similarities and differences between computer
and ITS road networks are studied. An exhaustive review of TDSP and k-SP
algorithms was conducted to classify and determine the best algorithms
and implementation procedures available in the literature. A new (heuristic)
algorithm (TD-kSP) that calculates multiple optimal paths for dynamic
networks is proposed and developed. A complete object-oriented computer
program in C++ was written using specialized network representations,
node-renumbering schemes and efficient path processing data structures
(classes) to implement this algorithm. A software environment where such
optimization algorithms can be applied in practice was then developed
using object-oriented design methodology. Extensive statistical and regression
analysis tests for various random network sizes, densities and other
parameters were conducted to determine the computational efficiency of
the algorithm. Finally, the algorithm was incorporated within the GIS-based
Wide-Area Incident Management Software System (WAIMSS) developed at the
Center for Transportation Research, Virginia Tech. The results of these
tests are used to obtain the empirical time-complexity of the algorithm.
Results indicate that the performance of this algorithm is comparable
to the best TDSP algorithms available in the literature, and strongly
encourages its possible application in real-time applications.
Complete testing of the algorithm requires the use of real-time link
flow data. While the use of randomly generated data and delay functions
in this study may not significantly affect its computational performance,
other measures of effectiveness as a routing tool remains untested. This
can be verified only if the algorithm itself becomes a part of the user-behavior
feedback loop. A closed loop traffic simulation/ system-dynamics study
would be required to perform this task. On the other hand, an open-loop
simulation would suffice for vehicle scheduling/dispatching problems.}}
@article{SugKat-IPSJ-85,
title = {{An algorithm for finding $k$ shortest loopless paths in a directed
network}},
author = {K. Sugimoto and Naoki Katoh},
journal = {Trans. Information Processing Soc. Japan},
volume = {26},
pages = {356--364},
year = {1985},
abstract = {This paper is concerned with a new algorithm for finding k
shortest loopless paths in a directed network. In this algorithm, multiple
loopless paths to the ending point are systematically represented by
a tree. It is known that there is no change in the order of the distance
between paths when some rules are changed for each link length in the
networks without changing the starting point of the path. The objective
paths can be obtained by efficiently growing the tree using this principle.
The authors describe the new algorithm, concrete examples in a model
network, measured values of calculation time in the grid-type network
and the comparison between the algorithm and existing algorithms. As
a result, it is proved that this is a very efficient and practically
effective algorithm.},
note = {In Japanese}}
@article{Suu-Nw-74,
title = {{Disjoint paths in a network}},
author = {J. W. Suurballe},
journal = {Networks},
volume = {4},
pages = {125--145},
year = {1974},
abstract = {Routes between two given nodes of a network are called diversified
if they are node-disjoint, except at the terminals. Diversified routes
are required for reliability in communication, and an additional criterion
is that their total cost, assumed to be the sum of individual arc lengths
or costs, is minimum. An algorithm and related theory is described for
a general number K of node-disjoint paths with minimum total length.
The algorithm applies shortest path labelling algorithms familiar in
the literature. K node-disjoint paths are found in K iterations of a
single shortest path algorithm.}}
@article{SuzTsuHir-JORSJ-87,
title = {{Water salesman problem}},
author = {H. Suzuki and M. Tsuji and R. Hirabayashi},
journal = {J. Oper. Res. Soc. Japan},
volume = {30},
number = {4},
pages = {472--492},
month = {December},
year = {1987},
abstract = {The shortest path problem is one of the classic and fundamental
problems in mathematical programming. Many real-world problems are formulated
as a shortest path problem and solved by a dynamic programming approach.
Recently there have been several studies on shortest path problems with
one or more knapsack type side constraints. In a constrained shortest
path problem every edge of the network has not only a distance but also
some weight such as time or cost. The paper concerns a type of constrained
shortest path problem in which the network has a weight imposed on its
nodes. For example, given a water price and its demand at every node,
the requirement is to find a sales route with maximal profit (=sales-cost)
that does not exceed the total supply Q. This is called the water salesman
problem. It is a subproblem derived from an existing vehicle routing
problem with supply constraints in a steel company. Two algorithms are
discussed for solving a generalized water salesman problem, including
the original one, where split deliveries of water are allowable. One
is based on dynamic programming where every state consists of two factors,
the current node and the remaining water supply. The other is an algorithm
using the k-th shortest path method. The algorithms are tested out on
randomly generated problems. The first algorithm can solve any water
salesman problem with 10 to 80 nodes but takes relatively more time.
The second one can solve almost all problems rapidly, but for some it
is forced to stop before obtaining the optimum solution because of memory
capacity.}}
@inproceedings{SzePev-RECOMB-97,
title = {{Las Vegas algorithms for gene recognition: suboptimal and error-tolerant
spliced alignment}},
author = {Sing-Hoi Sze and Pavel A. Pevzner},
booktitle = {Proc. 1st Int. Conf. Computational Molecular Biology},
publisher = {ACM},
pages = {300--309},
month = {January},
year = {1997}}
@inproceedings{TakBorLoe-WM-00,
title = {{Dealing with additional constraints in the $k$-shortest path
problem}},
author = {Tuomo Takkala and Ralf Bornd{\"o}rfer and Andreas L{\"o}bel},
booktitle = {Proc. WM 2000},
url = {http://www.cs.chalmers.se/~ilya/WM2000/proceedings.html},
abstract = {We discuss a method that deals with additional constraints
in a k-shortest path problem. These constraints can be of knapsack or
generalized covering type and model resources on subsets of the arcs
or the nodes. Our goal is to develop a method which handles these types
of constraints without changes in the k-shortest path code. Instead,
the cost coefficients (distances) of the arcs are modified and the resulting
problem is solved as usual. The basic idea is to impose penalties for
constraint violation and by that favor legal paths in the list of all
shortest paths.}}
@phdthesis{Tal-PhD-85,
title = {{Stochastic Network Evacuation Models}},
author = {Kayhan Talebi},
school = {Univ. of Massachusetts, Amherst, Dept. of Industrial Engineering},
year = {1985},
abstract = {Stochastic network evacuation models are crucial for the safe
evacuation of occupants from regions. Interest in stochastic models has
flourished only recently largely due to their cost effectiveness and
their ability to capture the overall egress process more realistically.
The overall objective of this thesis is to extend and complement the
recent developments in modeling egress problems via analytical queueing
networks. In the first part of this thesis, along with modeling the evacuation
problem with queueing networks, the existence of capacity limitations
at different locations in the egress network is addressed. An approximation
technique entitled the Expansion method is introduced for finite closed
queueing networks with single exponential servers. The approximation
technique is tested on networks with different topologies and the results
are validated by exact and simulation procedures. In the second part
of this thesis, the optimal routing problem within the stochastic framework
is discussed. Multi-objective integer programming formulations are presented
for both the uncapacitated and capacitated routing problems. The exact
procedures, however, are computationally intractable for most real world
problems due to the integer nature of the optimization problem. Three
heuristics based on the K-Shortest Path Algorithm are presented with
respect to two objectives: (1) Minimize total distance traveled, and
(2) Minimize maximum evacuation time. These heuristics are tested on
example egress networks and the results are presented. Finally, some
ideas and open questions are presented for future research in the area
of finite closed queueing networks and the optimal routing problem.}}
@phdthesis{Tan-PhD-95,
title = {{A Framework for Hierarchical Interactive Generation of Cellular{ }Layout{}}},
author = {Chi Tang},
school = {Rutgers Univ., Dept. Industrial Engineering},
year = {1995},
abstract = {Many manufacturing companies have adopted the concept of cellular
layout in system configurations to obtain efficiency, productivity, and
flexibility. A key factor in achieving these goals is the physical layout
of manufacturing cells on the factory floor. A 'good' cellular layout
design will not only reduce capital investment, but also eliminate unnecessary
activities. For general facility layout problems, researchers and practitioners
alike have developed numerous algorithms and procedures. However, most
of the existing methods ignore the flow directions and the cyclic routes
in flow analysis. Also, these methods usually treat machine cells and
storage areas as points or squares of equal size, with no or little consideration
for their geometric characteristics. Moreover, these methods do not explicitly
plan an efficient overall flow pattern to guide the layout process. This
is despite the fact that improving the material flow through system facilities
is one of the most important goals in manufacturing system layout design.
To address these issues, this study develops a flow-network based hierarchical
interactive approach that encapsulates many important considerations
of cellular layout planning. This approach can be systematically executed
in a three-phase design procedure. Phase 1 uses an extension of the K-Shortest
Path technique (Double-Sweep Method) to rationalize the various flows
of a system into a master flow network. Phase 2 plans a flow pattern
and designates the aisle structure for the system based on the master
flow network. Using a specially developed linear programming model, Phase
3 interactively locates and allocates the machine cells around the planned
flow pattern to generate layout solutions. The proposed method explicitly
considers the flow precedence in flow analysis and the geometric constraints
in the cell location and allocation process. Also, it integrates the
traffic aisle structure design into the layout process. In spite of its
comprehensiveness, the suggested approach is easy to apply and provides
flexibility to accommodate practical constraints.}}
@article{TanAbd-IJPR-96,
title = {{A framework for hierarchical interactive generation of cellular
layout}},
author = {Chi Tang and Layek L. Abdel-Malek},
journal = {Int. J. Production Res.},
volume = {34},
number = {8},
pages = {2133--2162},
month = {August},
year = {1996},
abstract = {This paper proposes a flow-network-oriented approach that hierarchically
addresses the problem of cellular layout design. It consists of three
major phases: 1) utilize the $k$-shortest path method to rationalize
the various flows of a system into a master flow network; 2) based on
this flow network, plan a flow pattern and designate the aisle structure
for the system; and 3) locate and allocate cells around the flow pattern
and aisle structure within a restricted floor plan. These three phases
compose an integrated interactive layout design process. The applicability
of this approach as well as its effectiveness is illustrated by case
studies.}}
@article{TanLia-JCUST-90,
title = {{A parallel algorithm for finding $K$ minimum spanning trees}},
author = {Ce Shan Tang and Wei Fa Liang},
journal = {J. China Univ. Sci. Tech.},
volume = {20},
number = {4},
pages = {464--471},
year = {1990}}
@inproceedings{TanZha-ICCT-98,
title = {{A study of two rerouting methods of link-restoration based selfhealing
algorithms in selfhealing networks}},
author = {Tang{ }Jian and Zhang{ }Huiming},
booktitle = {Proc. Int. Conf. Communication Technology},
publisher = {IEEE},
volume = {2},
year = {1998},
abstract = {In communication networks, single link failure is more frequent
than other failures. Link-restoration based selfhealing algorithms is
effective to single link failure. Among all rerouting methods of selfhealing
algorithms, KSP (K-shortest path) and KMF (K-maximum flow) are most important.
This approach presents a study of KSP and KMF. Computer experiments show
that, the rerouting ability of KSP and KMF are approximate to the maximum
and the rerouting ability of KMF is a little better than KSP. This result
reveals the good performance of KSP and KMF. It is helpful to choosing
a selfhealing algorithm with high restoration ratio.}}
@book{Tar-SIAM-83,
title = {{Data Structures and Network Algorithms}},
author = {Robert E. Tarjan},
series = {CBMS-NSF Regional Conference Series in Applied Mathematics},
publisher = {SIAM},
number = {44},
year = {1983}}
@inproceedings{TasTakMor-ASSP-94,
title = {{Efficient chart parsing of speech recognition candidates}},
author = {T. Tashiro and T. Takezawa and T. Morimoto and M. Nagata},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {2},
pages = {II/13--16},
month = {April},
year = {1994},
abstract = {In a spoken language system that uses the $N$-best interface
between the continuous-speech recognition component and the natural language
processing component, the role of the language processing component is
to filter speech recognition candidates and to determine the semantic
interpretation of the input. We propose as efficient chart parsing method
of finding the most plausible sentence within the $N$-best candidate
sentences and determining the semantic interpretation of the sentence,
while avoiding the re-computation of the common substrings. We use syntactic
and semantic constraints described in the unification-based framework
and context-sensitive conditional probability CFG preferences to reorder
the $N$-best candidates. In preliminary tests, our parser has been successful
in reducing parsing steps by sharing common substrings and in selecting
correct sentences first.}}
@article{Thu-ZOR-75,
title = {{A method for selecting the shortest path of a network}},
author = {R. Thumer},
journal = {Zeitschrift f{\"u}r Operations Research, Serie B (Praxis)},
volume = {19},
pages = {B149--153},
year = {1975},
abstract = {The method proposed can be used to avoid some of the well known
weaknesses of the generally applied algorithms for determining shortest
routes through networks by increasing their efficiency. Therefore it
is even possible to evaluate without much more effort the k best routes
in large networks. In addition bottlenecks can easily be taken into account.},
note = {In German}}
@inproceedings{Top-ICC-86,
title = {{A $k$-shortest path algorithm for adaptive routing in communications
networks}},
author = {Donald M. Topkis},
booktitle = {Int. Conf. Communications},
publisher = {IEEE},
volume = {1},
pages = {108--113},
year = {1986}}
@article{Top-TC-88,
title = {{A $k$-shortest path algorithm for adaptive routing in communications
networks}},
author = {Donald M. Topkis},
journal = {Trans. Communications},
publisher = {IEEE},
volume = {36},
number = {7},
pages = {855--859},
year = {1988},
review = {MR-89f-90057}}
@article{MR-89f-90057,
reviews = {Top-TC-88},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A $k$-shortest path algorithm for adaptive routing in communications
networks}},
author = {Peter Brucker},
volume = {89f},
number = {90057},
year = {1989},
text = {For a network with $n$ nodes and $e$ arcs an $O(ke \log n)$-algorithm
is given which finds the $k$ shortest paths with distinct initial links
from a particular node to all other nodes. Using Fibonacci heaps the
complexity can be improved to $O(kp \log(n)+ke)$. Under the assumption
that all arc lengths are equal to one an $O(ke)$-algorithm is developed.}}
@inproceedings{TraSeiSte-ICSLP-96,
title = {{A word graph based $N$-best search in continuous speech recognition}},
author = {B.-H. Tran and F. Seide and T. Steinbiss},
booktitle = {Proc. 4th Int. Conf. Spoken Language Processing},
publisher = {IEEE},
editor = {H. T. Bunnell and W. Idsardi},
volume = {4},
pages = {2127--2130},
month = {October},
year = {1996},
abstract = {The authors introduce an efficient algorithm for the exhaustive
search of N-best sentence hypotheses in a word graph. The search procedure
is based on a two-pass algorithm. In the first pass, a word graph is
constructed with standard time-synchronous beam search. The actual extraction
of N-best word sequences from the word graph takes place during the second
pass. With the implementation of a tree-organized N-best list, the search
is performed directly on the resulting word graph. Therefore, the parallel
bookkeeping of N hypotheses at each processing step during the search
is not necessary. It is important to point out that the proposed N-best
search algorithm produces an exact N-best list as defined by the word
graph structure. Possible errors can only result from pruning during
the construction of the word graph. In a postprocessing step, the N candidates
can be rescored with a more complex language model with highly reduced
computational cost. This algorithm is also applied in speech understanding
to select the most likely sentence hypothesis that satisfies some additional
constraints.}}
@phdthesis{Tse-PhD-97,
title = {{Towards a Framework for an Automated Landfill System}},
author = {Hui-Ping Tserng},
school = {Univ. of Wisconsin, Madison, Dept. of Civil Engineering},
year = {1997},
abstract = {This research developed a framework for an Automated Landfill
System (ALS). The automation characteristics of ALS offers significant
potential for increase in productivity, improvement in landfill space
management, and reduction in risk to workers in the landfill compaction
operation. The development of ALS requires: (1) Efficient space model
to maintain the landfill configuration, (2) Space management to monitor
landfill space consumption and achieve proper storage strategy, (3) Mapping
and positioning system to update landfill configuration in real-time,
(4) Instantaneous motion planning and controlling for multiple landfill
equipment, and (5) Measurement of in-situ waste density to avoid re-compaction.
This research focuses on the space model development, space model management,
multi-equipment motion planning, and a study of mapping and positioning
system. A 3-D Graphical Database System
(GDS) along with an Octree algorithm was developed as a space model
for a landfill site that will improve and assist the recovery program
as well as monitor the space usage of the landfill site. Space consumption
and waste information can be obtained easily by traversing the Octree
data structure via Octant's coding and property system. Furthermore,
Global Positioning System (GPS) technology can be used as a mapping and
positioning system to achieve the real-time space measurement for landfill
sites. An Instantaneous Motion Planning And Controlling Tool (IMPACT)
was developed to generate efficient and collision-free path for multiple
landfill equipment during the compaction operation. Each landfill equipment
will have a given starting point through which appropriate paths can
be determined while avoiding collisions with obstacles, other equipment,
and operators. The Quadtree-Cube algorithm, modified from Quadtree algorithm,
is proposed to address the motion planning for various types of landfill
equipment. The specific Network Graph can be extracted from the Quadtree-Cube
system for each piece of equipment. Then, IMPACT uses k-shortest path
algorithm to traverse the Network Graph. Subsequently, the IMPACT finds
a set of efficient and collision-free paths for each piece of landfill
equipment. An example application of IMPACT for landfill compaction operation
was also provided. The system has been implemented using a 3-D graphic
functional interface library--OpenGL, with C++ program binding.}}
@article{TsuShiOza-ECJ-75,
title = {{An algorithm for generating the cycles of a digraph}},
author = {S. Tsukiyama and I. Shirakawa and H. Ozaki},
journal = {Electronics and Communications in Japan},
volume = {58},
number = {4},
pages = {8--15},
month = {April},
year = {1975},
abstract = {Application of the proposed algorithm to a digraph G requires
memory space and processing time of the order of O(n+m+s) and O( nu mc+n+m),
respectively, where n, m and c are the numbers of vertices, edges and
cycles of G, s is the total length of cycles and nu maximum number of
vertices of strongly-connected nonseparable components in G. The algorithm
was programmed in FORTRAN and run on an IBM 370/165. Several implemented
examples revealing its efficiency are shown.}}
@article{TsuShiOza-IEICE-78,
title = {{On the algorithm to enumerate all the cutsets in a graph}},
author = {S. Tsukiyama and I. Shirakawa and H. Ozaki},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E61},
number = {7},
pages = {544},
month = {July},
year = {1978},
abstract = {Deals with the problem to enumerate all the cutsets in an undirected
graph, and presents a new linear time algorithm to this problem.}}
@article{TsuShiOza-IPSJ-75,
title = {{An algorithm for generating all the paths between two vertices
in a digraph and its application}},
author = {T. D. Am and S. Tsukiyama and I. Shirakawa and H. Ozaki},
journal = {Trans. Information Processing Soc. Japan},
volume = {16},
number = {9},
pages = {774--780},
year = {1975},
abstract = {Proposes a new efficient algorithm to generate all the paths
from a specified vertex to another one in a given directed graph. The
algorithm requires processing time of order $\Theta((n+m)(p+1))$ and
memory space of order $\Theta(n+m)$; where $n$, $m$, and $p$ denote the
numbers of vertices, edges, and directed paths to be sought of a graph.
As an application of the algorithm, this paper also considers the shortest
or the longest path problem in such a directed graph as contains cycle
of negative weight.},
note = {Did this version of the paper include Am as co-author?}}
@article{TsuShiOza-JACM-80,
title = {{An algorithm to enumerate all cutsets of a graph in linear time
per cutset}},
author = {S. Tsukiyama and I. Shirakawa and H. Ozaki and H. Ariyoshi},
journal = {J. Assoc. Comput. Mach.},
publisher = {ACM},
volume = {27},
number = {4},
pages = {619--632},
month = {October},
year = {1980},
abstract = {Deals with the problem or enumerating all the cutsets or all
the s-t cutsets separating two specified vertices s and t in an undirected
graph. A variety of approaches have been proposed for this problem, among
which one based on the partition of a set of vertices into two sets is
the most efficient. It is first shown that an algorithm of this type
has time complexity O((n+m)(n-log/sub 2/ mu ) mu ), and two new algorithms
with time complexity O((n+m)( mu +1)) are then proposed. One of these
new algorithms has space complexity O(n/sup 2/), and the other has space
complexity O(n+m), where n and m are the numbers of vertices and edges,
respectively, and mu is the number of s-t cutsets in a given graph. The
results of some computational experiments are also described. An investigation
is made of the extent to which the new algorithms are better, and how
good the performance of the old algorithm is, especially when a given
graph is 'dense', i.e., 2m/(n(n-1)){$>$}or=0.4.}}
@inproceedings{TsuShiOza-UJCC-75,
title = {{A survey: generating all the cycles of a digraph}},
author = {S. Tsukiyama and I. Shirakawa and H. Ozaki},
booktitle = {Proc. 2nd USA-Japan Computer Conf.},
publisher = {AFIPS},
pages = {92--96},
month = {August},
year = {1975},
abstract = {The generation of all the cycles of a digraph is fundamental
in the theory of graphs, and is also of great importance in the application
of digraph theory to computer science. The recent development of reducing
the computational labor in the problem of listing and counting the cycles
of a digraph is remarkable. The present paper surveys several representative
algorithms of the problem, and then proposes a new efficient method of
computational labor O(n+m) per cycle, with n and m representing the numbers
of vertices and edges of a digraph, respectively. The paper also observes
that the proposing algorithm can be applied with more efficiency than
any other especially to digraphs.}}
@inproceedings{VazYan-ICALP-92,
title = {{Suboptimal cuts -- their enumeration, weight and number}},
author = {Vijay V. Vazirani and Mihalis Yannakakis},
booktitle = {Proc. 19th Int. Coll. Automata, Languages, and Programming},
number = {623},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
pages = {366--377},
year = {1992},
note = {We present (1) an algorithm that enumerates the cuts of a network
by increasing weight with polynomial delay, and (2) an algorithm that
computes the k-th minimum weight in polynomial time for fixed k. We also
show that in the case of undirected networks there are only polynomially
many cuts that have the k-th minimum weight for any fixed k (whereas
directed networks can have exponentially many different minimum cuts).}}
@phdthesis{vdP-PhD-97,
title = {{Aspects of Sensitivity Analysis for the Traveling Salesman Problem}},
author = {Edo S. van der Poort},
school = {Univ. of Groningen, Dept. of Econometrics},
month = {6 November},
year = {1997},
note = {Discusses the computational complexity of sensitivity analysis
and $k$-best solutions for TSP problems. In the first half of this thesis,
van der Poort shows that these problems are just as hard to solve as
the TSP itself, but that algorithms for solving the TSP can be used to
determine the required sensitivity information. The second half examines
the relationship between stability and $k$-best problems for the TSP.}}
@article{VemKal-VLSI-95,
title = {{Generation of design verification tests from behavioral VHDL
programs using path enumeration and constraint programming}},
author = {R. Vemuri and R. Kalyanaraman},
journal = {Trans. VLSI Systems},
publisher = {IEEE},
volume = {3},
pages = {201--214},
year = {1995},
abstract = {A method for generation of design verification tests from behavior-level
VHDL programs is presented. The method generates stimuli to execute desired
control-flow paths in the given VHDL program. This method is based on
path enumeration, constraint generation and constraint solving Behavioral
VHDL programs contain multiple communicating processes, signal assignment
statements, and wait statements which are not found in traditional software
programming languages. Our model of constraint generation is specifically
developed for VHDL programs with such constructs. Control-flow paths
for which design verification tests are desired are specified through
certain annotations attached to the control statements in the VHDL programs.
These annotations are used to enumerate the desired paths. Each enumerated
path is translated into a set of mathematical constraints corresponding
to the statements in the path. Methods for generating constraint variables
corresponding to various types of carriers in VHDL and for mapping various
VHDL statements into mathematical relationships among these constraint
variables are developed. These methods treat spatial and temporal incarnations
of VHDL carriers as unique constraint variables thereby preserving the
semantics of the behavioral VHDL programs. Constraints are generated
in the constraint programming language CLP(R) and are solved using the
CLP(R) system. A solution to the set of constraints so generated yields
a design verification test sequence which can be applied for executing
the corresponding control path when the design is simulated. If no solution
exists, then it implies that the corresponding path can never be executed.
Experimental studies pertaining to the quality of path coverage and fault
coverage of the verification tests are presented.}}
@article{Vin-COSB-96,
title = {{Near-optimal sequence alignment}},
author = {Martin Vingron},
journal = {Current Opinion in Structural Biology},
volume = {6},
number = {3},
pages = {346--352},
month = {June},
year = {1996},
abstract = {Recent advances in algorithmic techniques and statistics of
sequence alignment have helped to make near-optimal alignments an important
tool in the delineation of biologically valid alignments. Near-optimal
alignments serve to judge the reliability of portions of a sequence alignment.
The statistical assessment of suboptimal alignment scores makes sequence
alignments less dependent on gap-penalty choice.}}
@mastersthesis{Voh-MS-90,
title = {{Diverse Routing in Network Planning}},
author = {Sonia Isabel Vohnout},
school = {Univ. of Arizona},
year = {1990},
abstract = {This thesis discusses an algorithm and two heuristics for solving
a particular network optimization problem: the node-disjoint paths problem.
The goal of this optimization problem is to find two node-disjoint paths
between a given origin-destination pair whose total cost is minimum.
This problem is shown to be NP-hard. Two heuristics are investigated
in this thesis. The sequential shortest paths heuristic is the faster
of the two methods, but the quality of the solution may be sacrificed.
On the other hand, the simultaneous shortest paths heuristic, which yields
very good solutions, has higher complexity. We also discuss an implicit
enumeration algorithm that is used to verify the quality of the solution
obtained from the heuristics.}}
@article{Wal-BIT-83,
title = {{On degeneracy in enumeration}},
author = {Stein W. Wallace},
journal = {BIT},
volume = {23},
number = {2},
pages = {267--270},
year = {1983},
review = {MR-84e-90062}}
@article{MR-84e-90062,
reviews = {Wal-BIT-83},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{On degeneracy in enumeration}},
volume = {84e},
number = {90062},
year = {1984},
text = {In the case of degeneracy in an LP-formulation, there is not a
one-to-one
correspondence between extreme points and feasible bases. If the task
is to find the $k$ best extreme points in the set of feasible solutions
to an LP, this lack of correspondence has a certain importance, since
methods based on the simplex algorithm are oriented towards feasible
bases instead of the relevant extreme points. We therefore present an
easily implementable method to avoid this problem.}}
@phdthesis{Wal-PhD-95,
title = {{Minimum Cost Routing in Stochastic Networks}},
author = {Kenneth Scott Walley},
school = {Univ. of California, Irvine, Dept. of Electronics and Electrical
Engineering},
year = {1995},
abstract = {An important management function in communication and computer
networks is the determination of the routes taken by incoming traffic
through the network. In route selection, costs are assigned to each potential
route, and the chosen route is determined from these costs. In this research,
models and analytical techniques are developed to estimate the costs
of virtual circuit routes in store and forward packet switched networks
in order to study routing behavior and improve routing algorithms. A
discrete-time stochastic queuing network model is considered first, and
analytic results are developed for the approximate occupancy probability
distribution of each stage along a tandem of infinite capacity queues
in which there are arrivals and departures at each stage. These results
improve upon previous discrete-time tandem analysis and are applied to
a virtual circuit routing algorithm with traffic prediction. In order
to limit the computational burden, candidate paths for analysis are preselected
using a k-shortest paths algorithm. Simulation studies show that improved
network delay performance is obtained for the routing algorithm considered
here over standard algorithms which use measured delay or mean occupancy
estimates based on Poisson traffic assumptions. A simple random network
model consisting of a G(n,p) random weighted graph where Prob(edge) =
p and edge costs are i.i.d. between different node pairs is also considered.
For the case of edge cost distributions which are discrete or which have
a general Taylor's series at zero cost, bounds, limit values, and some
exact results are determined for the probability distributions for the
shortest path cost, shortest path edge count, and the graph diameter.
These results are used to investigate properties of minimum cost routes.
An example using this model demonstrates the significant effect that
knowledge of the routed session traffic rate has on the routing performance
in virtual circuit routing. These results are also used to study for
more general random graph models than previously considered, the average
case performance benefits of two all-shortest paths algorithms in which
graph preprocessing to eliminate edges is used to reduce computations.}}
@techreport{Wal-RI-82,
title = {{Enumeration algorithm in linear programming}},
author = {Stein W. Wallace},
series = {Reports in Informatics},
institution = {Univ. of Bergen, Dept. of Informatics},
number = {3},
year = {1982},
review = {MR-84g-90062}}
@article{MR-84g-90062,
reviews = {Wal-RI-82},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Enumeration algorithm in linear programming}},
volume = {84g},
number = {90062},
year = {1984},
text = {Consider the linear programming problem: (1) Min $f(X)=C^T X$ subject
to $AX=a_0$, $X,a_0 \ge 0$, where $A$ is an $m\times n$ matrix and $rank(A)=rank(A,a_0)=m$.
$C$ and $X$ are $n$-vectors and $a_0$ is an $m$-vector. Let $X_{i_1}$
be an optimal solution to (1) with corresponding $f_{i_1}$. From $X_{i_1}$
we seek the $k$ best solutions to (1). By `best' we mean that if $i_1$,
$i_2$, $\ldots$, $i_k$ are the indices of the $k$ best extreme points,
then $f_{i_1} \le f_{i_2} \le\cdots\le f_{i_k}$ and $f_{i_j} \le f_{i_t}$
for all $j$, $t$ so that $j \le k < t \le r$, where $r$ is the total
number of extreme points. Solutions to this problem are often presented
as algorithms for finding all extreme points to (1). Such algorithms
are not always suitable when only a small number of extreme points is
asked for. The basis of our method is that of M. E. Dyer and L. G. Proll
[Math. Programming 12 (1977), 81 - 96; MR 57 {\#}18805]. Their algorithm
solves the problem of finding all the extreme points in the set of feasible
solutions to (1). We change the algorithm to solve the enumeration problem,
and in addition we make some important changes in the tests for neighbours.
We also prove that the algorithm works both as an enumeration algorithm
and as an algorithm for finding all extreme points. Whether we use perturbation
techniques or not, it is well known that degeneracies may produce several
versions of the same extreme point. Therefore we present a test to avoid
the same extreme point being registered several times among the $k$ best.
We also suggest how the problem of unbounded sets of feasible solutions
can be handled. One chapter is devoted to detailed algorithms and implementation
considerations, especially due to the fact that storage is often the
limiting factor in this kind of problem.}}
@article{WanIma-TIS-95,
title = {{A new approach of parsing and search based on the divide and
conquer strategy for continuous speech recognition}},
author = {Ming-Sheng Wang and S. Imai},
journal = {IEICE Trans. Information {\&} Systems},
volume = {E78-D},
number = {4},
pages = {455--465},
month = {April},
year = {1995},
abstract = {We report a new approach concerning a parsing and searching
problem for a given phonetic lattice. The approach is based on the divide
and conquer (DC) strategy. By dividing the phonetic lattice, we first
construct a PD-tree to represent this lattice, then, we parse through
this PD-tree to identify the possible sentence which is supposed to be
the speech utterance. Next, we propose a new search scheme called Downward
Request (DR) search model to decrease the computation costs, and this
search model gives us the optimal or $N$-best solutions. Experiments
performed on Chinese speech recognition show us the good results.}}
@article{Wat-NAS-83,
title = {{Sequence alignments in the neighborhood of the optimum}},
author = {Michael S. Waterman},
journal = {Proc. Natl. Acad. Sci. USA},
volume = {80},
pages = {3123--3124},
year = {1983}}
@article{WatBye-MB-85,
title = {{A dynamic programming algorithm to find all solutions in a neighborhood
of the optimum}},
author = {Michael S. Waterman and Thomas Hancock Byers},
journal = {Mathematical Biosciences},
volume = {77},
pages = {179--185},
year = {1985},
review = {MR-87c-90234}}
@article{MR-87c-90234,
reviews = {WatBye-MB-85},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{A dynamic programming algorithm to find all solutions in a neighborhood
of the optimum}},
volume = {87c},
number = {90234},
year = {1987},
text = {This paper describes a new technique for finding $K$th best policies
which modifies the usual backtracking procedure and lists all near-optimal
policies. This practical algorithm is very much in the spirit of the
original formulation of dynamic programming. An application to matching
biological sequences is given.}}
@article{WauDem-JSAC-96,
title = {{Design of the optical-path layer in multiwavelength cross-connected
networks}},
author = {N. Wauters and P. Demeester},
journal = {J. Selected Areas in Communications},
publisher = {IEEE},
volume = {14},
number = {6},
pages = {881--892},
month = {June},
year = {1996},
annote = {According to Sinclair \cite{Sin-ICT-98}, this paper describes
two routing algorithms, one of which is ``based on iterative application
of a modified version of Yen's k-shortest path algorithm, and aims to
produce the lowest cost allocation that still achieves minimum network
wavelength requirement.''}}
@inproceedings{Wei-ASSP-95,
title = {{LVCSR log-likelihood ratio scoring for keyword spotting}},
author = {M. Weintraub},
booktitle = {Proc. Int. Conf. Acoustics, Speech, and Signal Processing},
publisher = {IEEE},
volume = {1},
pages = {297--300},
month = {May},
year = {1995},
abstract = {A new scoring algorithm has been developed for generating wordspotting
hypotheses and their associated scores. This technique uses a large-vocabulary
continuous speech recognition (LVCSR) system to generate the $N$-best
answers along with their Viterbi alignments. The score for a putative
hit is computed by summing the likelihoods for all hypotheses that contain
the keyword normalized by dividing by the sum of all hypothesis likelihoods
in the $N$-best list. Using a test set of conversational speech from
Switchboard Credit Card conversations, we achieved an 81{\%} figure of merit
(FOM). Our word recognition error rate on this same test set is 54.7{\%}.}}
@article{Wei-Comp-76,
title = {{A new algorithm for the solution of the $k$-th best route problem}},
author = {M. M. Weigand},
journal = {Computing},
volume = {16},
pages = {139--151},
year = {1976},
abstract = {The algorithm for finding the k-shortest loopless paths from
one node to another is presented. Though memory need is less, the algorithm
is running about 20 times as fast on large networks (1000 nodes and more).
The computer time increases linearly with k and about quadratic with
the number of nodes on the generated paths.}}
@article{Wei-Nw-73,
title = {{The shortest and the $K$-shortest routes as assignment problems}},
author = {A. Weintraub},
journal = {Networks},
volume = {3},
pages = {61--73},
year = {1973},
review = {MR-54-9639}}
@article{MR-54-9639,
reviews = {Wei-Nw-73},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{The shortest and the $K$-shortest routes as assignment problems}},
volume = {54},
number = {9639},
year = {1977}}
@inproceedings{Wei-ORSA-72,
title = {{A shortest route algorithm with unrestricted costs on the arcs}},
author = {A. Weintraub},
booktitle = {Proc. 42nd Mtg. Operations Research Society of America},
journal = {Bull. Operations Research Soc. of America},
volume = {20},
pages = {B/334--335},
year = {1972},
abstract = {An algorithm for finding the shortest route between two nodes
in a network with unrestricted costs on the arcs is presented. The method
is based on solving an equivalent assignment problem. A parametric analysis
is presented. It is shown that if, after a shortest route is determined,
the costs on all arcs incident into or out of a node are modified in
any form, at most elementary calculations of order m-squared will determine
a new optimal solution. This feature, shared by Dynamic Programming algorithms
only for cases where all costs decrease, can be applied to problems such
as the determination of the K-shortest route and the K-smallest assignments
leading to upper bounds of order K-m-cubed in both cases.},
note = {Supplement 2}}
@article{WilJai-NRL-88,
title = {{An approach to postoptimality and sensitivity analysis of zero-one
goal programs}},
author = {G. R. Wilson and H. K. Jain},
journal = {Naval Research Logistics},
volume = {35},
pages = {73--84},
year = {1988},
abstract = {Presents a methodology for postoptimality and sensitivity analysis
of zero-one goal programs based on the set of k-best solutions. A method
for generating the set of k-best solutions using a branch and bound algorithm
and an implicit enumeration scheme for multiple objective problems are
discussed. Rules for determining the range of parameter changes that
still allows a member of the k-best set to be optimal are developed.
An investigation of a sufficient condition for postoptimality analysis
is also presented.}}
@article{Won-DM-79,
title = {{Semirings and path spaces}},
author = {A. Wongseelashote},
journal = {Discrete Mathematics},
volume = {26},
pages = {55--78},
year = {1979},
abstract = {This paper develops a unified algebraic theory for a class
of path problems such as that of finding the shortest or, more generally,
the k shortest paths in a network; the enumeration of elementary or simple
paths in a graph. It differs from most earlier work in that the algebraic
structure appended to a graph or a network of a path problem is not axiomatically
given as a starting point of the theory, but is derived from a novel
concept called a 'path space'. This concept is shown to provide a coherent
framework for the analysis of path problems, and hence the development
of algebraic methods for solving them.}}
@article{Won-Nw-76,
title = {{An algebra for determining all path-values in a network with
application to $k$-shortest-paths problems}},
author = {A. Wongseelashote},
journal = {Networks},
volume = {6},
pages = {307--334},
year = {1976},
abstract = {This paper presents an algebra which is appropriate for the
formulation and solution of k-shortest-paths problems. The algebra is
a generalization of 'Schedule Algebra' for computing path values in a
network. It is shown formally that these path values can be calculated
by using direct methods of numerical linear algebra for solving systems
of linear equations and an algorithm similar to the long division procedure
of ordinary arithmetic. Such a method is then modified to yield an algorithm
for finding k shortest elementary paths in a network.},
review = {MR-56-14628}}
@article{MR-56-14628,
reviews = {Won-Nw-76},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{An algebra for determining all path-values in a network with
application to $k$-shortest-paths problems}},
author = {E. Ja. Gabovic},
volume = {56},
number = {14628},
year = {1978}}
@inproceedings{WutOMa-ECOC-95,
title = {{A simple algorithm for wavelength assignment in optical networks}},
author = {L. Wuttisittikulkij and M. J. O'Mahony},
booktitle = {Proc. 21st Eur. Conf. Opt. Comm.},
pages = {859--862},
year = {1995},
annote = {According to Sinclair \cite{Sin-ICT-98}, this paper ``developed
a simple, fast and non-iterative algorithm, which works with k-lowest
hop count paths to obtain a low network wavelength requirement'' for optical
network routing.}}
@inproceedings{YamSekKub-IWPT-89,
title = {{An efficient enumeration algorithm of parses for ambiguous context-free
languages}},
author = {N. Yamai and T. Seko and N. Kubo and T. Kawata},
booktitle = {Proc. Int. Worksh. Parsing Technologies},
publisher = {Carnegie Mellon University},
pages = {286--296},
month = {August},
year = {1989},
abstract = {An efficient algorithm that enumerates parses of ambiguous
context-free languages is described, and its time and space complexities
are discussed. The paper first introduces a hierarchical graph suitable
for enumeration. Using this graph, enumeration of parses in the order
of acceptability is equivalent to finding paths of this graph in the
order of length. Then, an efficient enumeration algorithm is presented
with this graph, which can be applied to arbitrary context-free grammars.
For enumeration of $k$ parses in the order of the total weight of all
applied productions, the time and space complexities of the algorithm
are $O(n^3+kn^2)$ and $O(n^3+kn)$, respectively.}}
@article{Yen-MS-71,
title = {{Finding the $K$ shortest loopless paths in a network}},
author = {Jin Y. Yen},
journal = {Management Science},
volume = {17},
pages = {712--716},
year = {1971},
abstract = {Presents an algorithm for finding the K loopless paths that
have the shortest lengths from one node to another node in a network.
The significance of the new algorithm is that its computational upper
bound increases only linearly with the value of K. Consequently, in general,
the new algorithm is extremely efficient. This paper first reviews the
algorithms presently available for finding the K shortest loopless paths
in terms of the computational effort and memory addresses they require.
This is followed by the presentation of the new algorithm and its justification.
Finally, the efficiency of the new algorithm is examined and compared
with that of other algorithms.},
review = {MR-45-9827}}
@article{MR-45-9827,
reviews = {Yen-MS-71},
journal = {Mathematical Reviews},
publisher = {Amer. Math. Soc.},
title = {{Finding the $K$ shortest loopless paths in a network}},
author = {W.-K. Chen},
volume = {45},
number = {9827},
year = {1973}}
@inproceedings{Yen-ORSA-72,
title = {{Another algorithm for finding the $K$ shortest-loopless network
paths}},
author = {Jin Y. Yen},
booktitle = {Proc. 41st Mtg. Operations Research Society of America},
journal = {Bull. Operations Research Soc. of America},
volume = {20},
pages = {B/185},
year = {1972},
abstract = {This paper presents a new algorithm for finding the K loopless
paths from the origin to a sink that have the shortest lengths in the
network. The significance of the new algorithm is that it requires fewer
computations than other available algorithms proposed by Bock, Kantner
and Haynes (1957), Pollack (1961), Clarke, Krikorian, and Rausan (1963),
Sakarovitch (1968), and Yen (1971). A comparison of the efficiencies
of different algorithms is also presented.}}
@inproceedings{YenKuo-ASIIH-94,
title = {{Degraded gray-scale text recognition using pseudo-2D hidden Markov
models and $N$-best hypotheses}},
author = {Chinching Yen and Shyh-Shiaw Kuo},
booktitle = {Proc. Conf. Automatic Systems for the Identification and Inspection
of Humans},
number = {2277},
series = {Proc. SPIE},
publisher = {Int. Soc. Optical Engineering},
pages = {180--191},
month = {July},
year = {1994}}
@article{YenKuo-GMIP-95,
title = {{Degraded gray-scale text recognition using pseudo-2D hidden Markov
models and $N$-best hypotheses}},
author = {Chinching Yen and Shyh-Shiaw Kuo},
journal = {Graphical Models and Image Processing},
volume = {57},
number = {2},
pages = {131--145},
month = {March},
year = {1995},
abstract = {The pseudo-two-dimensional hidden Markov Model (PHMM), which
is an extension of the 1D HMM, has been shown to be an effective approach
in recognition of highly degraded and connected text. In this paper,
the PHMM is extended to directly recognize poorly printed gray-level
document images. The performance of the system is further enhanced by
the $N$-best hypotheses search, coupled with duration constraint. Experimental
results show that the new system has significantly improved the performance
when compared to a similar system using thresholded binary images as
inputs. The recognition rate improves from 97.7{\%} in the binary system
to 99.9{\%} in gray level with modified $N$-best search, over a testing
set with similar blur and noise conditions as the training set. For a
much more degraded testing set, it improves from 89.59 to 98.51{\%}. This
also demonstrates the robustness of the proposed system.}}
@inproceedings{YenKuo-ICIP-95,
title = {{On the use of duration-corrected $N$-best hypotheses for text
recognition in gray-scale document images}},
author = {Chinching Yen and Shyh-Shiaw Kuo},
booktitle = {Proc. Int. Conf. Image Processing},
publisher = {IEEE},
volume = {3},
pages = {332--335},
month = {October},
year = {1995},
abstract = {The pseudo two dimensional hidden Markov model (PHMM) is extended
to directly recognize poorly-printed gray-scale document images. The
$N$-best hypotheses search, coupled with duration correction, is also
developed to find best candidates. Experimental results have demonstrated
that the performance of the new system has been significantly improved
when compared to the original PHMM system [Kuo and Agazzi, 1994] using
binary images as inputs. The recognition rate improves from 97.7{\%} to
100{\%}, over a testing set with similar blur and noise conditions as the
training set. For a testing range far outside the training one, it improves
from 89.59{\%} to 98.51{\%}, which also demonstrates the robustness of the
proposed system.}}
@inproceedings{YuSec-GLSV-94,
title = {{Generation of colour-constrained spanning trees with application
in symbolic circuit analysis}},
author = {Q. C. Yu and C. Sechen},
booktitle = {Proc. 4th Great Lakes Symp. VLSI},
publisher = {IEEE},
pages = {252--255},
month = {March},
year = {1994}}
@article{YuSec-IJCTA-96,
title = {{Generation of colour-constrained spanning trees with application
in symbolic circuit analysis}},
author = {Q. C. Yu and C. Sechen},
journal = {Int. J. Circuit Theory {\&} Applications},
volume = {24},
number = {5},
pages = {597--603},
year = {1996},
abstract = {The main goal of approximate symbolic analysis of analogue
circuits is to find an approximate symbolic expression of limited size
for an arbitrary network function of a linear or linearized circuit in
the Laplace domain. In the classical two-graph tree enumeration approach,
finding the product terms in the symbolic network function corresponds
to finding the common spanning trees of a pair of graphs derived from
the circuit. A good step towards efficient approximation is to find the
important common trees without finding all of them. To simplify the problem,
we find important spanning trees of one graph and check them against
the other and retain common spanning trees only. For the symbolic expression
to be valid for a wide frequency range, capacitance-type edges have to
be distinguished from conductance-type edges. The problem can be abstracted
as the following: given a weighted undirected graph in which each edge
is either red or green, find the $K_i$ lowest weight spanning trees,
each of which has exactly $i$ red edges, in increasing order of weight
for all feasible $i$. We describe an efficient algorithm for this problem
which is an extension of one of the existing algorithms to generate spanning
trees in increasing order of weight, where no edge colour is introduced.
Implemented in a symbolic analysis programme are also presented.}}
@article{YuSec-TCAD-97,
title = {{Efficient approximation of symbolic network functions using matroid
intersection algorithms}},
author = {Q. C. Yu and C. Sechen},
journal = {Trans. Computer-Aided Design of Integrated Circuits {\&} Systems},
publisher = {IEEE},
volume = {16},
number = {10},
pages = {1073--1081},
month = {October},
year = {1997},
abstract = {An efficient and effective approximation strategy is crucial
to the success of symbolic analysis of large analog circuits. In this
paper we propose a new approximation strategy for the symbolic analysis
of linear circuits in the complex frequency domain. The strategy directly
generates common spanning trees of a two-graph in decreasing order of
tree admittance product, using matroid intersection algorithms. The strategy
reduces the total time for computing an approximate symbolic expression
in expanded format to polynomial with respect to the circuit size under
the assumption that the number of product terms retained in the final
expression is polynomial. Experimental results are clearly superior to
those reported in previous works.}}
@article{YuSec-TCS-96,
title = {{A unified approach to the approximate symbolic analysis of large
analog integrated circuits}},
author = {Q. C. Yu and C. Sechen},
journal = {Trans. Circuits and Systems},
publisher = {IEEE},
volume = {43},
number = {8},
pages = {656--669},
month = {August},
year = {1996},
note = {This paper describes a unified approach to the approximate symbolic
analysis of large linearized analog circuits in the complex frequency
domain. It combines two new approximation-during-computation strategies
with a variation of the classical two-graph tree enumeration method.
The first strategy is to generate common trees of the two-graphs, and
therefore the product terms in the symbolic network function, in the
decreasing order of magnitude. This is made possible by our algorithm
for generating color-constrained spanning trees in the order of weight.
It avoids the burden of computing all the product terms only to find
most of them numerically negligible. The second approximation strategy
is the sensitivity-based simplification of two-graphs, which excludes
from the two-graphs many of the insignificant circuit elements that have
little effect on the network function being derived. It significantly
reduces the complexity of the two-graphs before tree enumeration, Our
approach is therefore able to symbolically analyze much larger analog
integrated circuits than previously reported, using complete small signal
models for the semiconductor devices. We show accurate yet reasonably
sized symbolic network functions for integrated circuits with up to 39
transistors whereas previous approaches were limited to less than 15,
For even larger circuits, the limit is imposed mainly by the interpretability
of the generated symbolic network function.}}
@article{ZavZhaSch-TSAP-94,
title = {{A hybrid segmental neural net/hidden Markov model system for
continuous speech recognition}},
author = {G. Zavaliagkos and Y. Zhao and Richard Schwartz and J. Makhoul},
journal = {Trans. Speech {\&} Audio Processing},
publisher = {IEEE},
volume = {2},
number = {1, part 2},
pages = {151--160},
month = {January},
year = {1994},
abstract = {The current state-of-the-art in large-vocabulary, continuous
speech recognition is based on the use of hidden Markov models (HMM).
In an attempt to improve over HMM performance, the authors developed
a hybrid system that combines the advantages of neural networks and
HMM using a multiple hypothesis (or $N$-best) paradigm. The connectionist
component of the system, the segmental neural net (SNN), models all the
frames of a phonetic segment simultaneously, thus overcoming the well-known
conditional-independence limitation of the HMM. They describe the hybrid
system and discuss various aspects of SNN modeling, including network
architectures, training algorithms and context modeling. Finally, they
evaluate the hybrid system by performing several speaker-independent
experiments with the DARPA Resource Management (RM) corpus, and demonstrate
that the hybrid system shows a consistent improvement in performance
over the baseline HMM system.}}
@phdthesis{Zil-PhD-94,
title = {{Optimum Path Algorithms on Multidimensional Networks: Analysis,
Design, Implementation and Computational Experience}},
author = {Athanasios Kostantine Ziliaskopoulos},
school = {Univ. of Texas, Austin, Dept. of Civil Engineering},
year = {1994},
abstract = {This thesis is concerned with the problem of simultaneously
computing many paths between two nodes on networks with arcs characterized
by multiple attributes. These networks are referred to as multidimensional
networks and their properties are defined in this thesis. The motivation
is the emerging need for complex path algorithms arising from the development
of intelligent vehicle-highway systems (IVHS). A variety of problems
can be modeled and solved efficiently by the proposed approach: least-time
and least-cost path problems on networks with general time-dependent
arc costs, k-shortest path problems on uni- or multidimensional networks,
optimum path problems on networks with multiple user groups, intermodal
route planning problems, shortest path problems with penalties for intersection
movements, and stochastic shortest path problems. The general objective
of this thesis is to study the problem of computing optimum paths on
a multidimensional network from every node and dimensional element to
a destination node and a final dimensional element. One general approach
to model and solve these problems is to augment the network by adding
nodes and arcs, and applying conventional shortest path algorithms on
the resulting augmented network. However, augmentation is not always
possible, as in the case of continuous cost functions, and when it is
possible, it creates prohibitively large networks that are difficult
to represent, and code, and inflexible to alter. The proposed approach
does not require explicit expansion. It computes the paths for all the
dimensional elements simultaneously. It drives its efficiency by exploiting
the fact that the various dimensions share a common network topology.
The whole scheme can be easily expanded to include additional dimensions,
reflecting additional complexities of actual networks, without altering
the underlying network topology. The definition of the dimensions is
left open so the proposed approach is general and applicable to a broad
range of optimum path problems. For some dimension realizations, this
approach provides a solution to problems that were not addressed previously.
In other cases, it yields algorithms that are more efficient than existing
methods. The general solution approach is a dynamic programming approach,
both for the continuous and for the discrete time cases. The general
algorithms have computational disadvantages that restrict their applicability;
these disadvantages are identified and discussed along with a number
of common properties of the general optimum paths.}}
@article{ZilMah-TRB-96,
title = {{A note on least time path computation considering delays and
prohibitions for intersection movements}},
author = {Athanasios Kostantine Ziliaskopoulos and Hani S. Mahmassani},
journal = {Transportation Research, Part B. -- Methodological},
volume = {30},
number = {5},
pages = {359--367},
month = {October},
year = {1996},
note = {Most shortest path algorithms do not explicitly consider intersection
movements in calculating best paths. However, in congested street networks,
turning movement delays can be significant, and ignoring them may lead
to the calculation of suboptimal or illogical paths. To reflect turning
movements in practice, it is common to ''explode'' the network representation
for use with standard shortest path algorithms. This paper proposes
a considerably more efficient approach; it consists of an
extension to the commonly used forward star structure to represent the
network including intersection movements and movement prohibitions.
A label correcting shortest path algorithm is modified to take advantage
of the proposed representation and calculate the least time paths in
a computationally efficient way. The approach is implemented, tested
and compared with existing techniques. The application of similar modifications
to time-dependent and k-shortest path algorithms is also discussed.}}
@article{Zuk-JMB-91,
title = {{Suboptimal sequence alignment in molecular biology: alignment
with error analysis}},
author = {M. Zuker},
journal = {J. Mol. Biol.},
volume = {221},
number = {2},
pages = {403--420},
month = {September},
year = {1991},
abstract = {A molecular sequence alignment algorithm based on dynamic programming
has been extended to allow the computation of all pairs of residues that
can be part of optimal and suboptimal sequence alignments. The uncertainties
inherent in sequence alignment can be displayed using a new form of dot
plot. The method allows the qualitative assessment of whether or not
two sequences are related, and can reveal what parts of the alignment
are better determined than others. It also permits the computation of
representative optimal and suboptimal alignments. The relation between
alignment reliability and alignment parameters is discussed. Other applications
are to cyclical permutations of sequences and the detection of self-similarity.
An application to multiple sequence alignment is noted.}}
@article{Zuk-Sci-89,
title = {{On finding all suboptimal foldings of an RNA molecule}},
author = {M. Zuker},
journal = {Science},
volume = {244},
pages = {48--52},
month = {April},
year = {1989}}