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

The Shoshan-Zwick algorithm solves the all pairs shortest paths problem in undirected graphs with integer edge costs in the range {1, 2, . . . ,M}. It runs in Õ(M · n) time, where n is the number of vertices, M is the largest integer edge cost, and ω < 2.3727 is the exponent of matrix multiplication. It is the fastest known algorithm for this problem. This paper points out the erroneous behavior of the Shoshan-Zwick algorithm and revises the algorithm to resolve the issues that cause this behavior. Moreover, it discusses implementation aspects of the Shoshan-Zwick algorithm using currently-existing sub-cubic matrix multiplication algorithms.