2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 560-568

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

ABSTRACT

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.

INDEX TERMS

path-comparison-based algorithm, time bounds, all-pairs shortest paths, weighted graphs, hidden paths algorithm, edge weights, lower bound

CITATION

D.R. Karger,
D. Koller,
S.J. Phillips,
"Finding the hidden path: time bounds for all-pairs shortest paths",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 560-568, 1991, doi:10.1109/SFCS.1991.185419