SIAM Journal on Discrete Mathematics
Edge domination on bipartite permutation graphs and cotriangulated graphs
Information Processing Letters
Approximation algorithms
A 2-approximation algorithm for the minimum weight edge dominating set problem
Discrete Applied Mathematics
Edge dominating and hypomatchable sets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On approximability of the independent/connected edge dominating set problems
Information Processing Letters
Polyhedral techniques for graphic covering problems
Polyhedral techniques for graphic covering problems
Linear time 1/2 -approximation algorithm for maximum weighted matching in general graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Approximability of the capacitated b-edge dominating set problem
Theoretical Computer Science
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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 $\frac{1}{2}$-approximation algorithm for the weighted matching problem is also a 2-approximation algorithm for the unweighted b-EDS problem on general graphs.