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Breaking Row and Column Symmetries in Matrix Models

  • Pierre Flener
  • Alan M. Frisch
  • Brahim Hnich
  • Zeynep Kiziltan
  • Ian Miguel
  • Justin Pearson
  • Toby Walsh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2470)

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.

Keywords

Matrix Model Constraint Programming Constraint Satisfaction Problem Symmetry Class Partial Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Pierre Flener
    • 1
  • Alan M. Frisch
    • 2
  • Brahim Hnich
    • 3
  • Zeynep Kiziltan
    • 3
  • Ian Miguel
    • 2
  • Justin Pearson
    • 1
  • Toby Walsh
    • 4
  1. 1.Dept of Information TechUppsala UniversityUppsalaSweden
  2. 2.Department of Computer ScienceUniversity of YorkYorkEngland
  3. 3.Dept of Information ScienceUppsala UniversityUppsalaSweden
  4. 4.Cork Constraint Computation CentreUniversity College CorkCorkIreland

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