Complexity of approximating bounded variants of optimization problems

Authors:
Miroslav Chlebík;Janka Chlebíková
Affiliations:
Max Planck Institute for Mathematics in the Sciences, Inselstraße, Leipzig, Germany;Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, Bratislava, Slovakia
Venue:
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Year:
2006

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Abstract

We study low degree graph problems such as Maximum Independent Set and Minimum Vertex Cover. The goal is to improve approximation lower bounds for them and for a number of related problems like Max-B-Set Packing, Min-B-Set Cover, and Max-B-Dimensional Matching, B≥3. We prove, for example, that it is NP-hard to achieve an approximation factor of 95/94 for Max-3-DM, and a factor of 48/47 for Max-4-DM. In both cases the hardness result applies even to instances with exactly two occurrences of each element.