On Matrices, Automata, and Double Counting in Constraint Programming

Nicolas Beldiceanu 1, * Mats Carlsson 2 Pierre Flener 3 Justin Pearson 3
* Corresponding author
1 TASC - Theory, Algorithms and Systems for Constraints
LINA - Laboratoire d'Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique
Abstract : Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variablesM, with the same constraint C defined by a finitestate automaton A on each row ofMand a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We also provide a domain consistency filtering algorithm for the conjunction of lexicographic ordering constraints between adjacent rows ofMand (possibly different) automaton constraints on the rows. We evaluate the impact of our methods in terms of runtime and search effort on a large set of nurse rostering problem instances.
Document type :
Journal articles
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

Contributor : Contraintes Lina <>
Submitted on : Wednesday, November 28, 2012 - 6:17:08 PM
Last modification on : Friday, June 22, 2018 - 9:35:02 AM
Long-term archiving on : Saturday, December 17, 2016 - 5:48:47 PM


Files produced by the author(s)



Nicolas Beldiceanu, Mats Carlsson, Pierre Flener, Justin Pearson. On Matrices, Automata, and Double Counting in Constraint Programming. Constraints, Springer Verlag, 2013, 18 (1), pp.108-140. ⟨10.1007/s10601-012-9134-y⟩. ⟨hal-00758531⟩



Record views


Files downloads