A Framework for Decision-based Consistencies

International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones

Inverse Consistencies for Non-binary Constraints

We present a detailed study of two inverse consistencies for non-binary constraints: relational path inverse consistency (rel PIC) and pairwise inverse consistency (PWIC). These are stronger than generalized arc consistency (GAC), even though they also only prune domain values. We propose algorithms to achieve rel PIC and PWIC, that have a time complexity better than the previous generic algorithm for inverse consistencies. One of our algorithms for PWIC has a complexity comparable to that for GAC despite doing more pruning. Our experiments demonstrate that inverse consistencies can be more efficient than GAC on a range of non-binary problems