Extending Dual Arc Consistency

Comparisons between primal and dual approaches have recently been extensively studied and evaluated from a theoretical standpoint based on the amount of pruning achieved by each of these when applied to non-binary constraint satisfaction problems. Enforcing arc consistency on the dual encoding has been shown to strictly dominate enforcing GAC on the primal encoding (Stergiou & Walsh 1999). More recently, extensions to dual arc consistency have extended these results to dual encodings that are based on the construction of compact constraint coverings, that retain the completeness of the encodings, while using a fraction of the space. In this paper we present a complete theoretical evaluation of these different consistency techniques and also demonstrate how arbitrarily high levels of consistency can be achieved efficiently using them.

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