Approximation Algorithms for the Partition Vertex Cover Problem

  • Suman Kalyan Bera
  • Shalmoli Gupta
  • Amit Kumar
  • Sambuddha Roy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7748)

Abstract

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a 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-VC 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(logr), 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Suman Kalyan Bera
    • 1
  • Shalmoli Gupta
    • 2
  • Amit Kumar
    • 3
  • Sambuddha Roy
    • 1
  1. 1.IBM India Research LabNew DelhiIndia
  2. 2.University of Illinois at Urbana-ChampaignUSA
  3. 3.Indian Institute of Technology DelhiIndia

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