On approximation of max-vertex-cover

Abstract We consider the max-vertex-cover (MVC) problem, i.e., find k vertices from an undirected and edge-weighted graph G =( V , E ), where | V |= n ⩾ k , such that the total edge weight covered by the k vertices is maximized. There is a 3/4-approximation algorithm for MVC, based on a linear programming relaxation. We show that the guaranteed ratio can be improved by a simple greedy algorithm for k >(3/4) n , and a simple randomized algorithm for k >(1/2) n . Furthermore, we study a semidefinite programming (SDP) relaxation based approximation algorithms for MVC. We show that, for a range of k , our SDP-based algorithm achieves the best performance guarantee among the four types of algorithms mentioned in this paper.

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