Abstract
An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known toO(n/(logn)2). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strongsimultaneous performance guarantee for the clique and coloring problems.
The framework ofsubgraph-excluding algorithms is presented. We survey the known approximation algorithms for the independent set (clique), coloring, and vertex cover problems and show how almost all fit into that framework. We show that among subgraph-excluding algorithms, the ones presented achieve the optimal asymptotic performance guarantees.
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A preliminary version of this paper appeared in [9].
Supported in part by National Science Foundation Grant CCR-8902522 and PYI Award CCR-9057488.
Research done at Rutgers University. Supported in part by Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) fellowship.
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Boppana, R., Halldórsson, M.M. Approximating maximum independent sets by excluding subgraphs. BIT 32, 180–196 (1992). https://doi.org/10.1007/BF01994876
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DOI: https://doi.org/10.1007/BF01994876