Abstract
We study a variant of the maximum coverage problem which we label the maximum coverage problem with group budget constraints (MCG). We are given a collection of sets \({\cal S} = \{S_1, S_2, \ldots, S_m\}\) where each set S i is a subset of a given ground set X. In the maximum coverage problem the goal is to pick k sets from \({\cal S}\) to maximize the cardinality of their union. In the MCG problem \({\cal S}\) is partitioned into groupsG 1, G 2, ..., G ℓ. The goal is to pick k sets from \({\cal S}\) to maximize the cardinality of their union but with the additional restriction that at most one set be picked from each group. We motivate the study of MCG by pointing out a variety of applications. We show that the greedy algorithm gives a 2-approximation algorithm for this problem which is tight in the oracle model. We also obtain a constant factor approximation algorithm for the cost version of the problem. We then use MCG to obtain the first constant factor approximation algorithms for the following problems: (i) multiple depot k-traveling repairmen problem with covering constraints and (ii) orienteering problem with time windows when the number of time windows is a constant.
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Chekuri, C., Kumar, A. (2004). Maximum Coverage Problem with Group Budget Constraints and Applications. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_7
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DOI: https://doi.org/10.1007/978-3-540-27821-4_7
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