% 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}}