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New Results on Polynomial Inapproximabilityand Fixed Parameter Approximability of Edge Dominating Set

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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 dominatingset 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.

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Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, 75005, Paris, France

    Bruno Escoffier

  2. CNRS, UMR 7606, LIP6, 75005, Paris, France

    Bruno Escoffier

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

    Jérôme Monnot & Vangelis Th. Paschos

  4. Institut Universitaire de France, Paris, France

    Vangelis Th. Paschos

  5. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 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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Corresponding author

Correspondence to Bruno Escoffier.

Additional information

Research partially supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010, the National Natural Science Foundation of China under the Grant 61370071 and Fundamental Research Funds for the Central Universities under the Grant ZYGX2012J069. An extended abstract of the paper appears in the proceedings of IPEC’12, LNCS, volume 7535

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Escoffier, B., Monnot, J., Paschos, V.T. et al. New Results on Polynomial Inapproximabilityand Fixed Parameter Approximability of Edge Dominating Set . Theory Comput Syst 56, 330–346 (2015). https://doi.org/10.1007/s00224-014-9549-5

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  • DOI: https://doi.org/10.1007/s00224-014-9549-5

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