Propagation algorithms for lexicographic ordering constraints

Authors:
Alan M. Frisch;Brahim Hnich;Zeynep Kiziltan;Ian Miguel;Toby Walsh
Affiliations:
Department of Computer Science, University of York, UK;Faculty of Computer Science, Izmir University of Economics, Turkey;DEIS, University of Bologna, Italy;School of Computer Science, University of St Andrews, UK;National ICT Australia and Department of CS & E, UNSW, Australia
Venue:
Artificial Intelligence
Year:
2006

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Abstract

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.