A 6/5-approximation algorithm for the maximum 3-cover problem |
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Authors: | Ioannis Caragiannis Gianpiero Monaco |
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Affiliation: | 1. Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece 2. Department of Computer Science, University of L’Aquila, Via Vetoio, Coppito, 67100, L’Aquila, Italy
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Abstract: | ![]() In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial optimization problem with applications to resource allocation. We study the simplest APX-hard variant of the problem where all sets are of size at most 3 and we present a 6/5-approximation algorithm, improving the previously best known approximation guarantee. Our algorithm is based on the idea of first computing a large packing of disjoint sets of size 3 and then augmenting it by performing simple local improvements. |
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