Decomposable Constraints

Abstract

Many constraint satisfaction problems can be naturally and efficiently modelled using non-binary constraints like the “all-different” and “global cardinality” constraints. Certain classes of these non-binary constraints are “network decomposable” as they can be represented by binary constraints on the same set of variables. We compare theoretically the levels of consistency which are achieved on non-binary constraints to those achieved on their binary decomposition. We present many new results about the level of consistency achieved by the forward checking algorithm and its various generalizations to non-binary constraints. We also compare the level of consistency achieved by arc-consistency and its generalization to non-binary constraints, and identify special cases of non-binary decomposable constraints where weaker or stronger conditions, than in the general case, hold. We also analyze the cost, in consistency checks, required to achieve certain levels of consistency.KeywordsSearch TreeConsistency CheckConstraint Satisfaction ProblemTree DecompositionConstraint GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.