A 6/5-Approximation Algorithm for the Maximum 3-Cover Problem

Authors:
Ioannis Caragiannis;Gianpiero Monaco
Affiliations:
Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500;Department of Computer Science, University of L'Aquila, Coppito, Italy 67100
Venue:
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Year:
2008

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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 wsets 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.