On the Shoshan-Zwick Algorithm for the All-Pairs Shortest Path Problem
Vol. 21, no. 2, pp. 177-181, 2017. Concise paper.
Abstract The Shoshan-Zwick algorithm solves the all-pairs shortest paths problem in undirected graphs with integer edge costs in the range $\{1, 2, \dots, M\}$. It runs in $\tilde{O}(M\cdot n^{\omega})$ time, where $n$ is the number of vertices, $M$ is the largest integer edge cost, and $\omega < 2.3727$ is the exponent of matrix multiplication. It is the fastest known algorithm for this problem. This paper points out and corrects an error in the Shoshan-Zwick algorithm.
Submitted: August 2016.
Reviewed: November 2016.
Revised: December 2016.
Accepted: December 2016.
Final: December 2016.
Published: January 2017.
Communicated by Joseph S. B. Mitchell
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