Improved approximation bounds for edge dominating set in dense graphs

Authors:
Jean Cardinal;Stefan Langerman;Eythan Levy
Affiliations:
Computer Science Department, Université Libre de Bruxelles, CP212, B1050 Brussels, Belgium;Computer Science Department, Université Libre de Bruxelles, CP212, B1050 Brussels, Belgium;Computer Science Department, Université Libre de Bruxelles, CP212, B1050 Brussels, Belgium
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less than 2 in the cases where the input graph has n vertices and at least @e(n2) edges, for @e1/2. This ratio is shown to be asymptotically tight for @e1/2.