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International Colloquium on Automata, Languages, and Programming

ICALP 2006: Automata, Languages and Programming pp 274–285Cite as

Weighted Bipartite Matching in Matrix Multiplication Time

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

Research supported by KBN grant 1P03A01830.

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Author information

Authors and Affiliations

  1. Institute of Informatics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Piotr Sankowski

Authors
  1. Piotr Sankowski
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Sankowski, P. (2006). Weighted Bipartite Matching in Matrix Multiplication Time. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_25

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  • DOI: https://doi.org/10.1007/11786986_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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