Extending Dual Arc Consistency

Abstract

Many extensions to existing binary constraint satisfaction algorithms have been proposed that directly deal with nonbinary constraints. Another choice is to perform a structural transformation of the representation of the problem, so that the resulting problem is a binary CSP except that now the original constraints which were nonbinary are replaced by binary compatibility constraints between relations. A lot of recent work has focussed on comparing different levels of local consistency enforceable in the nonbinary representation with the dual representation. In this paper we present extensions to the standard dual encoding that can compactly represent the given CSP using an equivalent dual encoding that contains all the original solutions to the CSP, using constraint coverings. We show how enforcing arc consistency in these constraint covering based encodings, strictly dominates enforcement of generalized arc consistency (GAC) on the primal nonbinary encoding.