Maximum Coverage Problem with Group Budget Constraints and Applications

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, . . . , G . 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-t...

• Type: Conference
• Year: 2004
• Where: APPROX
• Authors: Chandra Chekuri, Amit Kumar
• Keywords: Algorithms, APPROX 2004, Constant Factor Approximation Algorithms, Maximum Coverage Problem, MCG Problem