Extending Dual Arc Consistency

Abstract

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.

Strong Inverse Consistencies for Non-Binary CSPs

“…A problem is ω-consistent iff any tuple in a constraint c i can be consistently extended to any other constraint c j and to all constraints c k such that var(c k ) ⊆ var(c i ) ∪ var(c j ) [9]. A problem is generalized dual arc consistent iff any tuple in a constraint c i can be consistently extended to any other constraint c j and satisfy all constraints c k such that…”

“…In contrast, little work had been done on such consistencies for non-binary constraints until very recently, whereas a number of consistencies that are stronger than GAC, but not domain filtering, have been developed. For example, pairwise consistency [7], hyper-m-consistency [8], relational consistency [11], and ω-consistency [9]. However, these consistencies are rarely used in practice, mainly because they have a high space complexity.…”

Partition search for non-binary constraint satisfaction

“…[23,63]. This may be helpful with binary constraints but it is certainly not necessary in the present context.…”