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 0 ` S such that the total cost of sets in S 0 does not exceed L, and the total weight of elements covered by S 0 is maximized. This problem is NP-hard. For the special case of this problem, where each set has unit cost, a (1 \Gamma 1 e )-approximation is known. Yet, no approximation results are known for the general cost version. The contribution of this paper is a (1 \Gamma 1 e )-approximation algorithm for the budgeted maximum coverage problem. We also argue that this approximation factor is the best possible, unless NP ` DT IME(n log log n ). 1 Introduction The budgeted maximum coverage problem is defined as follows. A collection of sets S = fS 1 ; S 2 ; : : : ; Sm g with associated costs fc i g m i=1 is defined over a domain of elements X = fx 1 ; x 2 ; : : : ; x n g with associated weights fw i ...

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