Elsevier

Discrete Mathematics

Volume 309, Issue 18, 28 September 2009, Pages 5739-5744
Discrete Mathematics

A note on submodular set cover on matroids

https://doi.org/10.1016/j.disc.2008.05.019Get rights and content
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Abstract

We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.

Keywords

Matroid
Independent sets
Set cover

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