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

Authors

  • Pavlos Eirinakis
  • Matthew Williamson
  • K. Subramani

DOI:

https://doi.org/10.7155/jgaa.00410

Keywords:

Shoshan-Zwick algorithm , all-pairs shortest path , certification , matrix multiplication

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.

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Published

2017-01-01

How to Cite

Eirinakis, P., Williamson, M., & Subramani, K. (2017). On the Shoshan-Zwick Algorithm for the All-Pairs Shortest Path Problem. Journal of Graph Algorithms and Applications, 21(2), 177–181. https://doi.org/10.7155/jgaa.00410

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