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Breaking row and column symmetries in matrix models

Flener, P., Frisch, A.M., Hnich, B., Kiziltan, Z., Miguel, I., Pearson, J. and Walsh, T. (2002) Breaking row and column symmetries in matrix models. In: Proceedings of the 8th International Conference on Principles and Practice of Constraint Programmin. Principles and Practice of Constraint Programming - (CP 2002), 9 - 13 September 2002, Ithaca, New York, USA. Lecture Notes in Computer Science (2470). Springer , Berlin / Heidelberg , pp. 462-477. ISBN 978-3-540-44120-5

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Abstract

We identify an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped. Whilst lexicographically ordering the rows (columns) breaks all the row (column) symmetries, lexicographically ordering both the rows and the columns fails to break all the compositions of the row and column symmetries. Nevertheless, our experimental results show that this is effective at dealing with these compositions of symmetries. We extend these results to cope with symmetries in any number of dimensions, with partial symmetries, and with symmetric values. Finally, we identify special cases where all compositions of the row and column symmetries can be eliminated by the addition of only a linear number of symmetry-breaking constraints.

Item Type: Proceedings Paper
Institution: The University of York
Academic Units: The University of York > Computer Science (York)
Depositing User: York RAE Import
Date Deposited: 27 Feb 2009 18:20
Last Modified: 27 Feb 2009 18:20
Published Version: http://dx.doi.org/10.1007/3-540-46135-3_31
Status: Published
Publisher: Springer
Identification Number: 10.1007/3-540-46135-3_31
URI: http://eprints.whiterose.ac.uk/id/eprint/7313

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