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

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

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