The complexity of global constraints

Authors:
Christian Bessiere;Emmanuel Hebrard;Brahim Hnich;Toby Walsh
Affiliations:
LIRMM, CNRS, Montpellier, France;Cork Constraint Computation Centre, University College Cork, Ireland;Cork Constraint Computation Centre, University College Cork, Ireland;Cork Constraint Computation Centre, University College Cork, Ireland
Venue:
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Year:
2004

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Abstract

We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, meta-constraints like the cardinality constraint, and learning nogoods.