Shortest Paths in Matrix Multiplication Time

[Extended Abstract]
  • Piotr Sankowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


In this paper we present an \({\tilde O}(W n^{\omega})\) time algorithm solving single source shortest path problem in graphs with integer weights from the set {–W,...,0,...,W}, where ω < 2.376 is the matrix multiplication exponent. For dense graphs with small edge weights, this result improves upon the algorithm of Goldberg that works in \({\tilde O}(mn^{0.5}{\rm log}W)\) time, and the Bellman-Ford algorithm that works in O(nm) time.


Short Path Matrix Multiplication Integer Weight Weighted Directed Graph Scaling Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Piotr Sankowski
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

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