Approximation Algorithms for the Submodular Hitting Set Problem

In this paper, we study the submodular hitting set problem (SHSP), which is a variant of the hitting set problem. In the SHSP, we are given a supergraph H = ( V , C ) and a nonnegative submodular function on the set 2 V . The objective is to determine a vertex subset to cover all hyperedges such that the cost of submodular covering is minimized. Our main work is to present a rounding algorithm and a primal-dual algorithm respectively for the SHSP and prove that they both have the approximation ratio k , where k is the maximum number of vertices in all hyperedges.