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A 6/5-approximation algorithm for the maximum 3-cover problem

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  • Ioannis Caragiannis

    (University of Patras)

  • Gianpiero Monaco

    (University of L’Aquila)

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.

Suggested Citation

  • Ioannis Caragiannis & Gianpiero Monaco, 2013. "A 6/5-approximation algorithm for the maximum 3-cover problem," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 60-77, January.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:1:d:10.1007_s10878-011-9417-z
    DOI: 10.1007/s10878-011-9417-z
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    References listed on IDEAS

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    2. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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