Approximation algorithms for partially covering with edges

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Approximation algorithms for partially covering with edges
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. The objective is given a bound on the total amount of penalties that one is permitted to pay, to find a minimum cost cover which respects this bound. We are given an 8/3-approximation for generalized partial EDS This result matches the best known guarantee for the {0, 1}-EDS problem, a specialization in only which 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-hard even though the standard...
Ojas Parekh
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Ojas Parekh
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