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arXiv · 1102.1006

On Approximating Four Covering and Packing Problems

Mary Ashley·Tanya Berger-Wolf·Piotr Berman·Wanpracha Chaovalitwongse·Bhaskar DasGupta·Ming-Yang Kao
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Abstract

In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results; this is done by directly transforming the inapproximability gap of Haastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or.

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BibTeXRIS

Mary Ashley, Tanya Berger-Wolf, Piotr Berman, Wanpracha Chaovalitwongse, Bhaskar DasGupta, Ming-Yang Kao. 2011-02-04. On Approximating Four Covering and Packing Problems. https://doi.org/10.1016/j.jcss.2009.01.002

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