On the all-pairs-shortest-path problem
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
On the complexity of the “most general” firing squad synchronization problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Improved algorithms for replacement paths problems in restricted graphs
Operations Research Letters
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The all-pairs shortest paths problem in weighted graphs is investigated. An algorithm called the hidden paths algorithm, which finds these paths in time O(m*+n n/sup 2/ log n), where m* is the number of edges participating in shortest paths, is presented. It is argued that m* is likely to be small in practice, since m*=O(n log n) with high probability for many probability distributions on edge weights. An Omega (mn) lower bound on the running time of any path-comparison-based algorithm for the all-pairs shortest paths problem is proved.