Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
High probability parallel transitive-closure algorithms
SIAM Journal on Computing
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
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
Improved parallel integer sorting without concurrent writing
Information and Computation
Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Improved algorithm for all pairs shortest paths
Information Processing Letters
Journal of Computer and System Sciences - Special issue: STOC 2003
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
A Shortest Path Algorithm for Real-Weighted Undirected Graphs
SIAM Journal on Computing
Regularity Lemmas and Combinatorial Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: { O(mn/log n) if m n log n log log log n O(mn log log n/log n) if m n log log n O(n2 log2 log n/log n) if m ≤ n log log n. These represent the best time bounds known for the problem for all m≪ n1.376. We also obtain a similar type of result for the diameter problem for unweighted directed graphs.