On Dual Encodings for Non-binary Constraint Satisfaction Problems

Abstract

In [Walsh and Stergiou, 1999] enforcing arc consistency (AC) in the dual encoding was shown to strictly dominate enforcing AC on the hidden or GAC on the original problem. We introduce a dual encoding that requires only a small subset of the original constraints to be stored in extension, while the remaining constraints can be stored intensionally. In this paper we present a theoretical comparison between the pruning achieved by enforcing AC on this dual encoding, versus enforcing GAC and dual arc consistency on the standard encoding. We show how the covering based encoding retains the dominance over enforcing GAC on the original problem, while using less space than the existing dual encoding.