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An O *(1.1939n) Time Algorithm for Minimum Weighted Dominating Induced Matching

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G = (V,E) is a subset of edges E′ ⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of finding a minimum weighted dominating induced matching, if any, and counting the number of dominating induced matchings of a graph with weighted edges. We describe an exact algorithm for general graphs that runs in O *(1.1939n) time and polynomial (linear) space, for solving these problems. This improves over the existing exact algorithms for the problems in consideration.

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Author information

Authors and Affiliations

  1. CONICET, Instituto de Cálculo and Departamento de Computación, Universidad de Buenos Aires, Buenos Aires, Argentina

    Min Chih Lin & Michel J. Mizrahi

  2. I. Mat., COPPE and NCE, Instituto Nacional de Metrologia, Qualidade e Tecnologia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Jayme L. Szwarcfiter

Authors
  1. Min Chih Lin
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  2. Michel J. Mizrahi
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  3. Jayme L. Szwarcfiter
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L. (2013). An O *(1.1939n) Time Algorithm for Minimum Weighted Dominating Induced Matching. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_52

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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