Optimization, approximation, and complexity classes

  • Authors:
  • Christos Papadimitriou;Mihalis Yannakakis

  • Affiliations:
  • University of California, San Diego;AT&T Bell Laboratories

  • Venue:
  • STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
  • Year:
  • 1988

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Abstract

We 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. We 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 under a kind of careful transformation (called L-reduction) that preserves approximability. It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does. These results may help explain the lack of progress on the approximability of a host of optimization problems.