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The Polynomially Bounded Perfect Matching Problem Is in NC 2

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STACS 2007 (STACS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4393))

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Abstract

The perfect matching problem is known to be in P, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations.

Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite graphs the problem of deciding the existence of a perfect matchings is in NC 2, and counting and enumerating all perfect matchings is in NC 3. For general graphs with a polynomially bounded number of perfect matchings, they show both problems to be in NC 3.

In this paper we extend and improve these results. We show that for any graph that has a polynomially bounded number of perfect matchings, we can construct all perfect matchings in NC 2. We extend the result to weighted graphs.

Supported by DFG grant Scho 302/7-1.

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Authors and Affiliations

  1. IIT Kanpur, India

    Manindra Agrawal

  2. Ulm University, Germany

    Thanh Minh Hoang

  3. Aalen University, Germany

    Thomas Thierauf

Authors
  1. Manindra Agrawal
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  2. Thanh Minh Hoang
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  3. Thomas Thierauf
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Wolfgang Thomas Pascal Weil

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Agrawal, M., Hoang, T.M., Thierauf, T. (2007). The Polynomially Bounded Perfect Matching Problem Is in NC 2 . In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_42

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  • DOI: https://doi.org/10.1007/978-3-540-70918-3_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70917-6

  • Online ISBN: 978-3-540-70918-3

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