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International Colloquium on Automata, Languages, and Programming

ICALP 2006: Automata, Languages and Programming pp 453–464Cite as

On the Bipartite Unique Perfect Matching Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4051))

Abstract

In this note, we give tighter bounds on the complexity of the bipartite unique perfect matching problem, bipartite-UPM. We show that the problem is in C = L and in NL  ⊕ L, both subclasses of NC 2.

We also consider the (unary) weighted version of the problem. We show that testing uniqueness of the minimum-weight perfect matching problem for bipartite graphs is in \({\rm \bf L}^{{\rm \bf C_=L}}\) and in NL  ⊕ L.

Furthermore, we show that bipartite-UPM is hard for NL.

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Author information

Authors and Affiliations

  1. Abt. Theor. Inform., Universität Ulm, 89069, Ulm, Germany

    Thanh Minh Hoang

  2. Inst. of Math. Sciences, Chennai, 600 113, India

    Meena Mahajan

  3. Fak. Elektr. und Inform., Aalen University, 73430, Aalen, Germany

    Thomas Thierauf

Authors
  1. Thanh Minh Hoang
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  2. Meena Mahajan
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  3. Thomas Thierauf
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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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Hoang, T.M., Mahajan, M., Thierauf, T. (2006). On the Bipartite Unique Perfect Matching Problem. 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_40

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  • DOI: https://doi.org/10.1007/11786986_40

  • 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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