Optimization, Approximation, and Complexity Classes


W e define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. W e show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete for MAXSNP under a kind of careful transformation (called L-redudon) that preserves approximability. It follows that such a complete problem has a polynomial-t ime approximation scheme iff the whole class does. These results may help explain the lack of progress on the approximabil ity of a host of optimization problems.

DOI: 10.1016/0022-0000(91)90023-X

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@article{Papadimitriou1991OptimizationAA, title={Optimization, Approximation, and Complexity Classes}, author={Christos H. Papadimitriou and Mihalis Yannakakis}, journal={J. Comput. Syst. Sci.}, year={1991}, volume={43}, pages={425-440} }