This survey on parallel algorithms emphasized the use of basic subroutines such as prefix sums, Euler tours, ear decomposition, and matrix multiplication for solving more complicated graph problems.
(BibTeX -- Citations -- CiteSeer -- ACM DL (ARCS) -- ACM DL (ICALP))
Characterizes two-terminal series graphs in terms of a tree-like structure in their ear decompositions. Uses this characterization to construct parallel algorithms that recognize these graphs and construct their series-parallel decompositions.
(BibTeX -- Citations -- MIT hypertext bibliography -- CiteSeer -- ACM DL)
Described slightly superlinear algorithms for partitioning a tree into a given number of subtrees, making them all as short as possible. Frederickson at the same conference further improved the sequential time to linear. There may still be something worth publishing in the parallel algorithms.
Speeds up the worst case time per pivot for various versions of the network simplex algorithm for minimum cost flow problems. Uses techniques from dynamic graph algorithms as well as some simple geometric data structures.
Describes data structures for maintaining the solution of a dynamically changing subset sum problem, and uses them to find a cut in a graph minimizing the difference between the heaviest and lightest cut edge.
We give a linear time algorithm for pruning a node-weighted tree to maximize the average node weight of the pruned subtree; this problem was previously studied under the less obvious name "The Fractional Prize-Collecting Steiner Tree Problem on Trees".
(BibTeX)
We consider a problem of assigning delays to components in a circuit so that each component is part of a critical path, but the number of edges belonging to critical paths is minimized. We show the problem to be NP-complete via a reduction from finding independent dominating sets in bipartite graphs minimizing dominated edges, and give experimental results on heuristics.
We survey problems in computational geometry that may be solved by constructing an auxiliary graph from the problem and solving a graph-theoretic problem on the auxiliary graph. The problems considered include the art gallery problem, partitioning into rectangles, minimum diameter clustering, bend minimization in cartogram construction, mesh stripification, optimal angular resolution, and metric embedding.
Shows both theoretically and experimentally that the number of times a random line crosses a road network is asymptotically upper bounded by the square root of the number of road segments.
Considers situations in which two hard approximation problems are presented by means of a single input. In many cases it is possible to guarantee that one or the other problem can be approximated to within a better approximation ratio than is possible for approximating it as a single problem. For instance, it is possible to find either a (1+ε)-approximation to a 1-2 TSP defined from a graph or a nε-approximation to the maximum independent set of the same graph, despite lower bounds showing nonexistence of approximation schemes for 1-2 TSP and nonexistence of approximations better than n1 − ε for independent set. However, for some other pairs of problems, such as hitting set and set cover, we show that solving the paired problem approximately is no easier than solving either problem independently.
We study relational event data in which a collection of actors in a social network have a sequence of pairwise interactions. Contiguous subsequences of these interactions form graphs, and we develop efficient data structures for querying the parameters of these graphs.
We give tight bounds on the size of the largest remaining grid minor in a grid graph from which a given number of vertices have been deleted, and study several related problems.
Graph Theory -- Publications -- David Eppstein -- Theory Group -- Inf. & Comp. Sci. -- UC Irvine
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