On Approximating Four Covering and Packing Problems

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 fullsibling 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 in [16, 19]; this is done by directly transforming the inapproximability gap of H˚astad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) [26] 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. [6, 7] and our results on the maximum profit coverage problem provides almost matching upper and...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Mary V. Ashley, Tanya Y. Berger-Wolf, Piotr Berman, Wanpracha Art Chaovalitwongse, Bhaskar DasGupta, Ming-Yang Kao
• Keywords: Approximability, CORR 2011, Education, Maximum Profit Coverage, NSF Grants