Counting, Structure Identification and Maximum Consistency for Binary Constraint Satisfaction Problems

Using a framework inspired by Schaefer's generalized satisfiability model [Sch78], Cooper, Cohen and Jeavons [CCJ94] studied the complexity of constraint satisfaction problems in the special case when the set of constraints is closed under permutation of labels and domain restriction, and precisely identified the tractable (and intractable) cases. Using the same model we characterize the complexity of three related problems: ffl counting the number of solutions. ffl structure identification (Dechter and Pearl [DP92]). ffl approximating the maximum number of satisfiable constraints. Keywords: constraint satisfaction, counting, structure identification, approximation. The University of Rochester Computer Science Department supported this work. 1 Introduction Determining consistency (satisfiability) of a constraint satisfaction problem is NP-complete in general [Mac77], even in the case when all constraints are binary. However, instances of constraint satisfaction that appear in pr..