The budgeted maximum coverage problem
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' subset of or equal to S such that the total cost of sets in S' does not exceed L, and the total weight of elements covered by SI 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 subset of or equal to DTIME(n(O(log log n))). (C) 1999 Published by Elsevier Science B.V. All rights reserved.
maximum coverage problem algorithms performance guarantee