Capacitated vertex covering

  • Authors:

  • Sudipto Guha;Refael Hassin;Samir Khuller;Einat Or

  • Affiliations:

  • Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA;Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel;Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD;Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel

  • Venue:
  • Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
  • 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) with weights on the vertices, the goal is to cover all the edges by picking a cover of minimum weight from the vertices. When we pick a copy of a vertex, we pay the weight of the vertex and cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is NP-hard. We give a primal-dual based approximation algorithm with an approximation guarantee of 2, and study several generalizations, as well as the problem restricted to trees.