Approximation algorithms for the maximum vertex coverage problem on bounded degree graphs

Abstract The Maximum Vertex Coverage problem (abbreviated as MVC) is to maximum the number of edges covered by a set of vertices of size exactly K on a graph. This problem is the dual of the vertex cover problem and has attracted a lot of interests in the literature of approximation algorithm. So far, the best approximation factor for the MVC problem is 3/4, which is obtained using an LP-rounding method. The main results of this paper are new approximation algorithms for MVC on cubic graphs and 3-bounded graphs (the vertex degrees are at most 3). The approximation factor on cubic graphs is 79/90 (≈0.878), which is tight by analyzing the existence of a feasible solution for a linear programming system. This algorithm can also be extended to 3-bounded graphs and guarantees an approximation factor of 19/24 (≈0.792).