Abstract
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.
We are very thankful to Warwick Harvery, Nicolas Beldiceanu, the members of the APES research group (especially Ian Gent, Patrick Prosser, and Barbara Smith), and Pierre Flener for valuable discussions on this work. The algorithm described herein is the subject of British Patent Application No. 0205606.7. This research was made possible by VR grant 221-99-369, EPSRC grant GR/N16129 and an EPSRC advanced research fellowship.
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Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T. (2002). Global Constraints for Lexicographic Orderings. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_7
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DOI: https://doi.org/10.1007/3-540-46135-3_7
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