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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A preliminary version of this paper appeared in Proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science (MFCS’08).
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Caragiannis, I., Monaco, G. A 6/5-approximation algorithm for the maximum 3-cover problem. J Comb Optim 25, 60–77 (2013). https://doi.org/10.1007/s10878-011-9417-z
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DOI: https://doi.org/10.1007/s10878-011-9417-z