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Propagation algorithms for lexicographic ordering constraints

Frisch, A. M., Hnich, B., Kiziltan, Z., Miguel, I. and Walsh, T. (2006) Propagation algorithms for lexicographic ordering constraints. Artificial Intelligence, 170 (10). 803 - 834. ISSN 0004-3702

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Finite-domain constraint programming has been used with great success to tackle a wide variety of combinatorial problems in industry and academia. To apply finite-domain constraint programming to a problem, it is modelled by a set of constraints on a set of decision variables. A common modelling pattern is the use of matrices of decision variables. The rows and/or columns of these matrices are often symmetric, leading to redundancy in a systematic search for solutions. An effective method of breaking this symmetry is to constrain the assignments of the affected rows and columns to be ordered lexicographically. This paper develops an incremental propagation algorithm, GACLexLeq, that establishes generalised arc consistency on this constraint in O(n) operations, where n is the length of the vectors. Furthermore, this paper shows that decomposing GACLexLeq into primitive constraints available in current finite-domain constraint toolkits reduces the strength or increases the cost of constraint propagation. Also presented are extensions and modifications to the algorithm to handle strict lexicographic ordering, detection of entailment, and vectors of unequal length. Experimental results on a number of domains demonstrate the value of GACLexLeq.

Item Type: Article
Keywords: Artificial intelligence; Constraints; Constraint programming; Constraint propagation; Lexicographic ordering; Symmetry; Symmetry breaking; Generalized arc consistency; Matrix models
Institution: The University of York
Academic Units: The University of York > Computer Science (York)
Depositing User: York RAE Import
Date Deposited: 17 Aug 2009 16:03
Last Modified: 17 Aug 2009 16:03
Published Version: http://dx.doi.org/10.1016/j.artint.2006.03.002
Status: Published
Publisher: Elsevier Science B.V., Amsterdam
Identification Number: 10.1016/j.artint.2006.03.002
URI: http://eprints.whiterose.ac.uk/id/eprint/5686

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