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- Published 1991 in J. Comput. Syst. Sci.

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.

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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}
}