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Polynomial-Delay and Polynomial-Space Enumeration of Large Maximal Matchings

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Graph-Theoretic Concepts in Computer Science (WG 2022)

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Abstract

Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings in specific orders. In this paper, we present polynomial-delay enumeration algorithms for maximal matchings with cardinality at least given threshold t. Our algorithm enumerates all such matchings in O(nm) delay with exponential space, where n and m are the number of vertices and edges of an input graph, respectively. We also present a polynomial-delay and polynomial-space enumeration algorithm for this problem. As a variant of this algorithm, we give an algorithm that enumerates k-best maximal matchings that runs in polynomial-delay.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Yasuaki Kobayashi

  2. Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Kazuhiro Kurita

  3. Department of Computer Science and Engineering, Toyohashi University of Technology, Aichi, Japan

    Kunihiro Wasa

Authors
  1. Yasuaki Kobayashi
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  2. Kazuhiro Kurita
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  3. Kunihiro Wasa
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Corresponding author

Correspondence to Kazuhiro Kurita .

Editor information

Editors and Affiliations

  1. University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Universität Tübingen, Tübingen, Germany

    Michael Kaufmann

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Kobayashi, Y., Kurita, K., Wasa, K. (2022). Polynomial-Delay and Polynomial-Space Enumeration of Large Maximal Matchings. In: Bekos, M.A., Kaufmann, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2022. Lecture Notes in Computer Science, vol 13453. Springer, Cham. https://doi.org/10.1007/978-3-031-15914-5_25

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  • DOI: https://doi.org/10.1007/978-3-031-15914-5_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15913-8

  • Online ISBN: 978-3-031-15914-5

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