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arXiv · 1112.1945

Approximation Algorithms for Edge Partitioned Vertex Cover Problems

Suman Kalyan Bera·Shalmoli Gupta·Amit Kumar·Sambuddha Roy
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Abstract

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each partition $P_i$. The goal is to find a minimum cost set of vertices which cover at least $k_i$ edges from the partition $P_i$. We call this the Partition Vertex Cover problem. In this paper, we give matching upper and lower bound on the approximability of this problem. Our algorithm is based on a novel LP relaxation for this problem. This LP relaxation is obtained by adding knapsack cover inequalities to a natural LP relaxation of the problem. We show that this LP has integrality gap of $O(log r)$, where $r$ is the number of sets in the partition of the edge set. We also extend our result to more general settings.

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Suman Kalyan Bera, Shalmoli Gupta, Amit Kumar, Sambuddha Roy. 2012-10-10. Approximation Algorithms for Edge Partitioned Vertex Cover Problems. https://arxiv.org/abs/1112.1945

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