On Approximating an Implicit Cover Problem in Biology

Authors:
Mary V. Ashley;Tanya Y. Berger-Wolf;Wanpracha Chaovalitwongse;Bhaskar Dasgupta;Ashfaq Khokhar;Saad Sheikh
Affiliations:
Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607;Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607;Department of Industrial Engineering, Rutgers University, Piscataway, NJ 08855;Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607;Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607;Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607
Venue:
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Year:
2009

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Abstract

In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly. For example, the well-known minimum feedback arc set problem is such a problem. In this paper, we consider such a cover problem that arises in the study of wild populations in biology in which the sets are defined implicitly via the Mendelian constraints and prove approximability results for this problem.