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A Tight Analysis of the Maximal Matching Heuristic

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Computing and Combinatorics (COCOON 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3595))

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Abstract

We study the worst-case performance of the maximal matching heuristic applied to the Minimum Vertex Cover and Minimum Maximal Matching problems, through a careful analysis of tight examples. We show that the tight worst-case approximation ratio is asymptotic to \({\rm min}\, \{2, 1/(1-\sqrt{1-\epsilon})\}\) for graphs with an average degree at least εn and to min {2, 1/ε} for graphs with a minimum degree at least εn.

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Author information

Authors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Jean Cardinal, Martine Labbé, Stefan Langerman & Eythan Levy

  2. Université de Mons-Hainaut, Belgium

    Hadrien Mélot

Authors
  1. Jean Cardinal
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  2. Martine Labbé
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  3. Stefan Langerman
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  4. Eythan Levy
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  5. Hadrien Mélot
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Lusheng Wang

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© 2005 Springer-Verlag Berlin Heidelberg

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Cardinal, J., Labbé, M., Langerman, S., Levy, E., Mélot, H. (2005). A Tight Analysis of the Maximal Matching Heuristic. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_71

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  • DOI: https://doi.org/10.1007/11533719_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28061-3

  • Online ISBN: 978-3-540-31806-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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