Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Computing dominances inEn (short communication)
Information Processing Letters
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
All pairs shortest paths for graphs with small integer length edges
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
All pairs shortest distances for graphs with small integer length edges
Information and Computation
Rectangular matrix multiplication revisited
Journal of Complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algebraic Structures and Algorithms for Matching and Matroid Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Theoretical Computer Science
All-pairs bottleneck paths for general graphs in truly sub-cubic time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
All-pairs bottleneck paths in vertex weighted graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding a heaviest triangle is not harder than matrix multiplication
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for path problems in weighted graphs
Efficient algorithms for path problems in weighted graphs
Weighted bipartite matching in matrix multiplication time
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
More effective crossover operators for the all-pairs shortest path problem
Theoretical Computer Science
Hi-index | 0.00 |
Given a directed graph with a capacity on each edge, the all-pairs bottleneck paths (APBP) problem is to determine, for all vertices s and t, the maximum flow that can be routed from s to t. For dense graphs this problem is equivalent to that of computing the (max, min)-transitive closure of a real-valued matrix. In this paper, we give a (max, min)-matrix multiplication algorithm running in time O(n(3+ω)/2) ≤ O(n2.688), where ω is the exponent of binary matrix multiplication. Our algorithm improves on a recent O(n2+ω/3) ≤ O(n2.792)- time algorithm of Vassilevska, Williams, and Yuster. Although our algorithm is slower than the best APBP algorithm on vertex capacitated graphs, running in O(n2.575) time, it is just as efficient as the best algorithm for computing the dominance product, a problem closely related to (max, min)-matrix multiplication. Our techniques can be extended to give subcubic algorithms for related bottleneck problems. The all-pairs bottleneck shortest paths problem (APBSP) asks for the maximum flow that can be routed along a shortest path. We give an APBSP algorithm for edge-capacitated graphs running in O(n(3+ω)/2) time and a slightly faster O(n2.657)-time algorithm for vertex-capactitated graphs. The second algorithm significantly improves on an O(n2.859)-time APBSP algorithm of Shapira, Yuster, and Zwick. Our APBSP algorithms make use of new hybrid products we call the distance-max-min product and dominance-distance product.