Improved Approximation Algorithm for Minimum Weight k-Subgraph Cover Problem

Abstract

For a graph G, a vertex subset C is a Connected k-Subgraph Cover (VCC) if every connected subgraph on k vertices of G contains at least one vertex from C. Using local ratio method, a -approximation algorithm was given in [14] for the minimum weight VCC problem under the assumption that the girth g(G) (the length of a shortest cycle of G) is at least k. In this paper, we prove that a -approximation can be achieved when and. Although our algorithm also employs the local ratio method, the analysis has a big difference from that in [14], this is why the girth constraint can be relaxed from k to 2k/3.