Abstract
We introduce a formal framework for studying approximation properties of NP optimization (NPO) problems. The classes we consider are those appearing in the literature, namely the class of approximable problems within a constant ε (APX), the class of problems having a Polynomial-time Approximation Scheme (PAS) and the class of problems having a Fully Polynomial-time Approximation Scheme (FPAS). We define natural approximation preserving reductions and obtain completeness results for these classes. A complete problem in a class can not have stronger approximation properties unless P=NP. We also show that the degree structure of NPO allows intermediate degrees, that is, if P≠NP, there are problems which are neither complete nor belong to a lower class.
This work was done when the author was at Dipartimento di Informatica e Sistemistica, Via Buonarroti 12, 00185 Roma Italy
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© 1989 Springer-Verlag Berlin Heidelberg
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Crescenzi, P., Panconesi, A. (1989). Completeness in approximation classes. In: Csirik, J., Demetrovics, J., Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1989. Lecture Notes in Computer Science, vol 380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51498-8_11
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DOI: https://doi.org/10.1007/3-540-51498-8_11
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