An improved approximation algorithm for vertex cover with hard capacities

  • Authors:

  • Rajiv Gandhi;Eran Halperin;Samir Khuller;Guy Kortsarz;Aravind Srinivasan

  • Affiliations:

  • Department of Computer Science, Rutgers University, Camden, NJ 08102, USA;International Computer Science Institute, Berkeley, CA 94704, USA and Computer Science Division, University of California, Berkeley, CA 94720, USA;Department of Computer Science, University of Maryland, College Park, MD 20742, USA and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA;Department of Computer Science, Rutgers University, Camden, NJ 08102, USA;Department of Computer Science, University of Maryland, College Park, MD 20742, USA and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2006

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Abstract

We study the capacitated vertex cover problem, a generalization of the well-known vertex-cover problem. Given a graph G=(V,E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex-cover problem. Previously, approximation algorithms with an approximation factor of 2 were developed with the assumption that an arbitrary number of copies of a vertex may be chosen in the cover. If we are allowed to pick at most a fixed number of copies of each vertex, the approximation algorithm becomes much more complex. Chuzhoy and Naor (FOCS, 2002) have shown that the weighted version of this problem is at least as hard as set cover; in addition, they developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of three and matching (up to lower-order terms) the best approximation ratio known for the vertex-cover problem.