Nonbinary Constraint Satisfaction: From the Dual to the Primal

Non binary constraints have recently been studied quite extensively since they represent real life problems very naturally. Specifically, extensions to binary arc consistency into generalised arc consistency (GAC), and forward checking that incorporates a limited amount of GAC have been proposed, to handle non-binary constraints directly. Enforcing arc consistency on the dual encoding has been shown to strictly dominate nforcing GAC on the primal encoding. More recently, modifications to dual arc consistency have extended these results to dual encodings that are based on the construction of compact onstraint coverings, that retain the completeness of the encodings, while using a fraction of the space. In this paper we present results that combine the enforcement of arc consistency in these covering based dual encodings, with performing forward checking based search in the primal encoding. We demonstrate how this new scheme can be shown to strictly dominate standard non-binary forward checking, while being able to efficiently enforce extremely high levels of consistency.