Approximating edge dominating set in dense graphs

  • Authors:

  • Richard Schmied;Claus Viehmann

  • Affiliations:

  • Department of Computer Science, University of Bonn;Department of Computer Science, University of Bonn

  • Venue:
  • TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
  • Year:
  • 2011

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Abstract

We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ε-dense and average ε-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the Minimum Edge Dominating Set problem in everywhere ε-dense and average ε-dense graphs by using the techniques of Karpinski and Zelikovsky, the approximation ratios of min{2, 3/(1+2ε)} and of min{2, 3/(3-2√1 -ε)}, respectively. On the other hand, we show that it is UGC-hard to approximate the Minimum Edge Dominating Set problem in everywhere ε-dense graphs with a ratio better than 2/(1 + ε) with ε 1/3 and 2/(2 -√1 - ε) with ε 5/9 in average ε-dense graphs.