All pairs shortest paths in undirected graphs with integer weights

Avi Shoshan*, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

109 Scopus citations


We show that the All Pairs Shortest Paths (APSP) problem for undirected graphs with integer edge weights taken from the range {1, 2, ..., M} can be solved using only a logarithmic number of distance products of matrices with elements in the range {1, 2,..., M}. As a result, we get an algorithm for the APSP problem in such graphs that runs in Ō(Mn$+ω/) time, where n is the number of vertices in the algorithm of Galil and Margalit.

Original languageEnglish
Pages (from-to)605-614
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1999
EventProceedings of the 1999 IEEE 40th Annual Conference on Foundations of Computer Science - New York, NY, USA
Duration: 17 Oct 199919 Oct 1999

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