Capacitated vertex covering

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.  2003 Elsevier Inc. All rights reserved.