A Probabilistic Study of Bound Consistency for the Alldifferent Constraint

Jérémie Du Boisberranger 1 Danièle Gardy 1 Charlotte Truchet 2, * Xavier Lorca 2, *
* Corresponding author
2 TASC - Theory, Algorithms and Systems for Constraints
LINA - Laboratoire d'Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique
Abstract : This paper introduces a mathematical model for bound consistency of the con- straint AllDifferent. It allows us to compute the probability that the filtering algorithm effectively removes at least one value in the variable domains. A complete study of the bound consistency properties is then proposed. It identifies several behaviors depending on some macroscopic quantities related to the variables and the domains. Finally, it is shown that the probability for an AllDifferent constraint to be bound consistent can be asymptotically estimated in constant time. The experiments illustrate that the precision is good enough for a practical use in constraint programming.
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Submitted on : Tuesday, April 26, 2011 - 7:35:29 PM
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Jérémie Du Boisberranger, Danièle Gardy, Charlotte Truchet, Xavier Lorca. A Probabilistic Study of Bound Consistency for the Alldifferent Constraint. 2011. ⟨hal-00588888⟩

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