Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
D.R. Karger , Dept. of Comput. Sci., Stanford Univ., CA, USA
D. Koller , Dept. of Comput. Sci., Stanford Univ., CA, USA
S.J. Phillips , Dept. of Comput. Sci., Stanford Univ., CA, USA
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.
path-comparison-based algorithm, time bounds, all-pairs shortest paths, weighted graphs, hidden paths algorithm, edge weights, lower bound
D. Karger, D. Koller and S. Phillips, "Finding the hidden path: time bounds for all-pairs shortest paths,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 560-568.