New Results on Polynomial Inapproximabilityand Fixed Parameter Approximability of Edge Dominating Set

Abstract : An edge dominating set in a graph $G = (V, E)$ is a subset $S$ of edges such that each edge in $E - S$ is adjacent to at least one edge in $S$. The edge dominating set problem, to find an edge dominating set of minimum size, is a basic and important NP-hard problem that has been extensively studied in approximation algorithms and parameterized complexity. In this paper, we present improved hardness results and parameterized approximation algorithms for edge dominating set. More precisely, we first show that it is NP-hard to approximate edge dominating set in polynomial time within a factor better than $1.18$. Next, we give a parameterized approximation schema (with respect to the standard parameter) for the problem and, finally, we develop an $O^\ast(1.821^\tau)$-time exact algorithm where $\tau$ is the size of a minimum vertex cover of $G$.
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Theory of Computing Systems, Springer Verlag, 2015, 56 (2), pp.330-346. 〈http://link.springer.com/article/10.1007/s00224-014-9549-5〉. 〈10.1007/s00224-014-9549-5〉
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https://hal.archives-ouvertes.fr/hal-01200585
Contributeur : Bruno Escoffier <>
Soumis le : mercredi 16 septembre 2015 - 16:50:21
Dernière modification le : vendredi 31 août 2018 - 09:25:57

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Bruno Escoffier, Jérôme Monnot, Vangelis Paschos, Mingyu Xiao. New Results on Polynomial Inapproximabilityand Fixed Parameter Approximability of Edge Dominating Set. Theory of Computing Systems, Springer Verlag, 2015, 56 (2), pp.330-346. 〈http://link.springer.com/article/10.1007/s00224-014-9549-5〉. 〈10.1007/s00224-014-9549-5〉. 〈hal-01200585〉

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