A Complete Classification of the Approximability of Maximization Problems Derived from Boolean Constraint Satisfaction

Abstract

In this paper we study the approximability of boolean constraint satisfaction problems. A problem in this class consists of some collection of "constraints" (i.e., functions f : f0; 1g k ! f0; 1g); an instance of a problem is a set of constraints applied to specified subsets of n boolean variables. Schaefer earlier studied the question of whether one could find in polynomial time a setting of the variables satisfying all constraints; he showed that every such problem is either in P or is NP-complete. We consider optimization variants of these problems in which one either tries to maximize the number of satisfied constraints (as in MAX 3SAT or MAX CUT) or tries to find an assignment satisfying all constraints which maximizes the number of variables set to 1 (as in MAX CUT or MAX CLIQUE). We completely classify the approximability of all such problems. In the first case, we show that any such optimization problem is either in P or is MAX SNP-hard. In the second case, we show that such ..

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Last time updated on 22/10/2014

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