an:01771664
Zbl 1002.68203
Khuller, Samir; Moss, Anna; Naor, Joseph
The budgeted maximum coverage problem
EN
Inf. Process. Lett. 70, No. 1, 39-45 (1999).
00087251
1999
j
68W25 68W40 68Q17
budgeted maximum coverage problem
Summary: 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 \(S'\) of \(S\) such that the total cost of the sets in \(S'\) does not exceed \(L\), and the total weight of the 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 \(\text{NP}\subseteq\text{DTIME}(n^{O(\log\log n)})\).