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Abstract

Max CSP( P ) is the problem of maximizing the weight of satisfied constraints, where each constraint acts over a k-tuple of literals and is evaluated using the predicate P. The approximation ratio of a random assignment is equal to the fraction of satisfying inputs to P. If it is NP-hard to achieve a better approximation ratio for Max CSP( P ), then we say that P is approximation resistant. Our goal is to characterize which predicates that have this property.

A general approximation algorithm for Max CSP( P ) is introduced. For a multitude of different P, it is shown that the algorithm beats the random assignment algorithm, thus implying that P is not approximation resistant. In particular, over 2/3 of the predicates on four binary inputs are proved not to be approximation resistant, as well as all predicates on 2s binary inputs, that have at most 2s+1 accepting inputs.

We also prove a large number of predicates to be approximation resistant. In particular, all predicates of arity 2s+s 2 with less than \(2^{s^2}\) non-accepting inputs are proved to be approximation resistant, as well as almost 1/5 of the predicates on four binary inputs.

Keywords

Random Assignment Constraint Satisfaction Problem Satisfying Assignment Annual IEEE Symposium Hard Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Gustav Hast
    • 1
  1. 1.Department of Numerical Analysis and Computer ScienceRoyal Institute of TechnologyStockholmSweden

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