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

  • Venue:
  • ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
  • Year:
  • 2003

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Abstract

In this paper 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, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002 ) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also 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 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.