Approximating edge dominating set in dense graphs

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. © 2011 Springer-Verlag.