Decomposable Constraints

Ian Philip Gent, K Stergiou, T Walsh

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 nonbinary 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 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, and we present experimental results on benchmark domains that demonstrate the practical usefulness of our theoretical analysis. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)133-156
Number of pages24
JournalArtificial Intelligence
Publication statusPublished - Oct 2000


  • constraint satisfaction
  • search
  • decomposable constraints
  • generalized arc consistency
  • maintaining arc consistency


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