The budgeted maximum coverage problem

Abstract The budgeted maximum coverage problem is: given a collection S of sets with associated costs defined over a domain of weighted elements, and a budget L , find a subset of S ′⫅ S such that the total cost of sets in S ′ does not exceed L , and the total weight of elements covered by S ′ is maximized. This problem is NP-hard. For the special case of this problem, where each set has unit cost, a (1−1/ e ) -approximation is known. Yet, prior to this work, no approximation results were known for the general cost version. The contribution of this paper is a (1−1/ e ) -approximation algorithm for the budgeted maximum coverage problem. We also argue that this approximation factor is the best possible, unless NP ⫅ DTIME (n O ( log log n) ) .