On the Shoshan-Zwick Algorithm for the All-Pairs Shortest Path Problem

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.