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.
This work was partially supported by the EU COST Action 293 “Graphs and Algorithms in Communication Networks” (GRAAL), by the EU IST FET Integrated Project 015964 AEOLUS, and by a “Caratheodory” research grant from the University of Patras.
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Caragiannis, I., Monaco, G. (2008). A 6/5-Approximation Algorithm for the Maximum 3-Cover Problem. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_16
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DOI: https://doi.org/10.1007/978-3-540-85238-4_16
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