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Maximal Matching and Path Matching Counting in Polynomial Time for Graphs of Bounded Clique Width

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Theory and Applications of Models of Computation (TAMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6648))

Abstract

In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal matchings, we introduce matching-cover pairs to efficiently handle maximality in the local structure, and develop a polynomial time algorithm. For path matchings, we develop a way to classify the path matchings in a polynomial number of equivalent classes. Using these, we develop dynamic programing algorithms that run in polynomial time of the graph size, but in exponential time of the clique-width. In particular, we show that for a graph G of n vertices and clique-width k, these problems can be solved in O(n f(k)) time where f is exponential in k or in O(n g(l)) time where g is linear or quadratic in l if an l-expression for G is given as input.

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Author information

Authors and Affiliations

  1. ENS Lyon, France

    Benjamin Hellouin de Menibus

  2. National Institute of Informatics, Tokyo, 101–8430, Japan

    Takeaki Uno

Authors
  1. Benjamin Hellouin de Menibus
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  2. Takeaki Uno
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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de Menibus, B.H., Uno, T. (2011). Maximal Matching and Path Matching Counting in Polynomial Time for Graphs of Bounded Clique Width. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_47

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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