New results on polynomial inapproximability and fixed parameter approximability of edge dominating set

  • Authors:

  • Bruno Escoffier;Jérôme Monnot;Vangelis Th. Paschos;Mingyu Xiao

  • Affiliations:

  • LAMSADE, CNRS UMR 7243, PSL Research University, Université Paris-Dauphine, France;LAMSADE, CNRS UMR 7243, PSL Research University, Université Paris-Dauphine, France;LAMSADE, CNRS UMR 7243, PSL Research University, Université Paris-Dauphine, France,Institut Universitaire de France, France;School of Computer Science and Engineering, University of Electronic Science and Technology of China, China

  • Venue:
  • IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
  • Year:
  • 2012

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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.