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Journal of the ACM (JACM)
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The lexicographic decision function
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Propagation algorithms for lexicographic ordering constraints
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AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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Propagation algorithms for lexicographic ordering constraints
Artificial Intelligence
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PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
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CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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AI'05 Proceedings of the 18th Canadian Society conference on Advances in Artificial Intelligence
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Finite domain bounds consistency revisited
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IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Short and long supports for constraint propagation
Journal of Artificial Intelligence Research
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We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show that decomposing such constraints carries a penalty either in the amount or the cost of constraint propagation. We therefore present a global consistency algorithm which enforces a lexicographic ordering between two vectors of n variables in O(nb) time, where b is the cost of adjusting the bounds of a variable. The algorithm can be modified very slightly to enforce a strict lexicographic ordering. Our experimental results on a number of domains (balanced incomplete block design, social golfer, and sports tournament scheduling) confirm the efficiency and value of these new global constraints.