SIAM Journal on Discrete Mathematics
Combinatorial optimization
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
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Approximability of the capacitated b-edge dominating set problem
Theoretical Computer Science
A primal-dual approximation algorithm for partial vertex cover: making educated guesses
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
The prize-collecting edge dominating set problem in trees
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
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The edge dominating set (EDS) and edge-cover (EC) problems are classical graph covering problems in which one seeks a minimum cost collection of edges which covers the edges or vertices, respectively, of a graph. We consider the generalized partial cover version of these problems, in which failing to cover an edge, in the EDS case, or vertex, in the EC case, induces a penalty. Given a bound on the total amount of penalties that we are permitted to pay, the objective is to find a minimum cost cover with respect to this bound. We give an 8/3-approximation for generalized partial EDS. This result matches the best-known guarantee for the {0,1}-EDS problem, a specialization in which only a specified set of edges need to be covered. Moreover, 8/3 corresponds to the integrality gap of the natural formulation of the {0,1}-EDS problem. Our techniques can also be used to derive an approximation scheme for the generalized partial edge-cover problem, which is NP-complete even though the uniform penalty version of the partial edge-cover problem is in P.