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New Results on Polynomial Inapproximability and Fixed Parameter Approximability of edge dominating set

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Parameterized and Exact Computation (IPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7535))

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Abstract

An edge dominating set in a graph G = (V,E) is a subset S of edges such that each edge in E − S is adjacent to at least one edge in S. The edge dominating set problem, to find an edge dominating set of minimum size, is a basic and important NP-hard problem that has been extensively studied in approximation algorithms and parameterized complexity. In this paper, we present improved hardness results and parameterized approximation algorithms for edge dominating set. More precisely, we first show that it is NP-hard to approximate edge dominating set in polynomial time within a factor better than 1.18. Next, we give a parameterized approximation schema (with respect to the standard parameter) for the problem and, finally, we develop an O *(1.821τ)-time exact algorithm where τ is the size of a minimum vertex cover of G.

Research partially supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010 and the National Natural Science Foundation of China under the Grant 60903007.

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Authors and Affiliations

  1. LAMSADE, CNRS UMR 7243, PSL Research University, Université Paris-Dauphine, France

    Bruno Escoffier, Jérôme Monnot & Vangelis Th. Paschos

  2. Institut Universitaire de France, France

    Vangelis Th. Paschos

  3. School of Computer Science and Engineering, University of Electronic Science and Technology of China, China

    Mingyu Xiao

Authors
  1. Bruno Escoffier
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  2. Jérôme Monnot
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  3. Vangelis Th. Paschos
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  4. Mingyu Xiao
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Dimitrios M. Thilikos

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Escoffier, B., Monnot, J., Paschos, V.T., Xiao, M. (2012). New Results on Polynomial Inapproximability and Fixed Parameter Approximability of edge dominating set . In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

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