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Weighted Bipartite Matching in Matrix Multiplication Time

[Extended Abstract]
  • Piotr Sankowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

In this paper we consider the problem of finding maximum weighted matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problem work in \(\tilde{O}(Wn^{\omega})\) time, where ω is the matrix multiplication exponent, and W is the highest edge weight in the graph. As a consequence of this result we obtain \(\tilde{O}(Wn^{\omega})\) time algorithms for computing: minimum weight bipartite vertex cover, single source shortest paths and minimum weight vertex disjoint s-t paths.

Keywords

Perfect Match Vertex Cover Minimum Vertex Cover Weighted Directed Graph Vertex Disjoint Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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