Abstract
We consider a multiple domination version of the edge dominating set problem, called the b-EDS problem, where an edge set D ⊆ E of minimum cardinality is sought in a given graph G = (V,E) with a demand vector b ∈ ℤE such that each edge e ∈ E is required to be dominated by b(e) edges of D. When a solution D is not allowed to be a multi-set, it is called the simple b-EDS problem. We present 2-approximation algorithms for the simple b-EDS problem for the cases of max e ∈ E b(e) = 2 and max e ∈ E b(e) = 3. The best approximation guarantee previously known for these problems is 8/3 due to Berger et al. [2] who showed the same guarantee to hold even for the minimum cost case and for arbitrarily large b. Our algorithms are designed based on an LP relaxation of the b-EDS problem and locally optimal matchings, and the optimum of b-EDS is related to either the size of such a matching or to the optimal LP value.
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Fujito, T. (2014). On Matchings and b-Edge Dominating Sets: A 2-Approximation Algorithm for the 3-Edge Dominating Set Problem. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_18
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DOI: https://doi.org/10.1007/978-3-319-08404-6_18
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