Linear Time Algorithms for Generalized Edge Dominating Set Problems

Abstract. In this paper we consider a generalization of the edge dominating set (EDS) problem, in which each edge e needs to be covered be times and refer to this as the b-EDS problem. We present an exact linear time primal dual algorithm for the weighted b-EDS problem on trees with be ∈ {0, 1}, and our algorithm generates an optimal dual solution as well. We also present an exact linear time algorithm for the unweighted b-EDS problem on trees. For general graphs we exhibit a relationship between this problem and the maximum weight matching problem. We exploit this relationship to show that a known linear time 1 2 -approximation algorithm for the weighted matching problem is also a 2-approximation algorithm for the unweighted b-EDS problem on general graphs.

• Type: Conference
• Year: 2005
• Where: WADS
• Authors: André Berger, Ojas Parekh
• Keywords: Algorithm, Algorithms, B-EDS Problem, Exact Linear Time, WADS 2005