Improved Approximation Bounds for Edge Dominating Set in Dense Graphs [chapter]

Jean Cardinal, Stefan Langerman, Eythan Levy
2007 Lecture Notes in Computer Science  
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 'n 2´e dges, for > 1/2. This ratio is shown to be asymptotically tight for > 1/2.
doi:10.1007/11970125_9 fatcat:n4kvqo4oerfyday24dappnllee