Approximation of the Quadratic Set Covering problem

Authors:
Bruno Escoffier;Peter L. Hammer
Affiliations:
Lamsade, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cédex 16, France;RUTCOR, Rutgers, The State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA
Venue:
Discrete Optimization
Year:
2007

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Abstract

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant). Then we focus on the convex case and give both positive and negative approximation results. Finally, we tackle the unweighted version of this problem.