A Slightly Improved Sub-Cubic Algorithm for the All Pairs Shortest Paths Problem with Real Edge Lengths

Authors:
Uri Zwick
Affiliations:
Department of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Algorithmica
Year:
2006

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Abstract

We present an $O(n^3\sqrt{\log\log n}/\!\log n)$-time algorithm for the All Pairs Shortest Paths (APSP) problem for directed graphs with real edge lengths. This slightly improves previous algorithms for the problem obtained by Fredman, Dobosiewicz, Han, and Takaoka.