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 S = {S1,S2, . . . , Sm} where each set Si is a subset of a given ground set X. In the maximum coverage problem the goal is to pick k sets from S to maximize the cardinality of their union. In the MCG problem S is partitioned into groups G1, G2, . . . , Gℓ. The goal is to pick k sets from 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. © Springer-Verlag 2004.
CITATION STYLE
Chekuri, C., & Kumar, A. (2004). Maximum coverage problem with group budget constraints and applications. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3122, 72–83. https://doi.org/10.1007/978-3-540-27821-4_7
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