SIAM Journal on Discrete Mathematics
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Edge domination on bipartite permutation graphs and cotriangulated graphs
Information Processing Letters
Handbook of combinatorics (vol. 1)
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
A Unified Approach to Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Approximation algorithms for the b-edge dominating set problem and its related problems
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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We study the approximability of the weighted edge-dominating set problem. Although even the unweighted case is NP-Complete, in this case a solution of size at most twice the minimum can be efficiently computed due to its close relationship with minimum maximal matching; however, in the weighted case such a nice relationship is not known to exist. In this paper, after showing that weighted edge domination is as hard to approximate as the well studied weighted vertex cover problem, we consider a natural strategy, reducing edge-dominating set to edge cover. Our main result is a simple 2 1/10 -approximation algorithm for the weighted edge-dominating set problem, improving the existing ratio, due to a simple reduction to weighted vertex cover, of 2rWVC, where rWVC is the approximation guarantee of any polynomial-time weighted vertex cover algorithm. The best value of rWVC currently stands at 2- log log |V|/2 log |V|. Furthermore we establish that the factor of 2 1/10 is tight in the sense that it coincides with the integrality gap incurred by a natural linear programming relaxation of the problem.