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J. Puget (1993)
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
J. Crawford, M. Ginsberg, E. Luks, Amitabha Roy (1996)
Symmetry-Breaking Predicates for Search Problems
T. Walsh, C. Bessiere, Alan Frisch, E. Hébrard, Brahim Hnich, Z. Kiziltan, Ian Miguel (2006)
Symmetry Breaking
Barbara Smith (2005)
Sets of Symmetry Breaking Constraints
X. Tan (2004)
TECHNICAL RESEARCH REPORT
D. Cohen, P. Jeavons, Christopher Jefferson, K. Petrie, Barbara Smith (2005)
Symmetry Definitions for Constraint Satisfaction ProblemsConstraints, 11
Ian Gent, Barbara Smith (1999)
Symmetry breaking during search in constraint programming
Alan Frisch, Warwick Harvey (2003)
Constraints for Breaking All Row and Column Symmetries in a Three-by-Two Matrix
P. Flener, A. Frisch, Brahim Hnich, Z. Kiziltan, Ian Miguel, J. Pearson, T. Walsh (2001)
Symmetry in matrix models
Alan Frisch, Christopher Jefferson, Ian Miguel (2003)
Constraints for Breaking More Row and Column Symmetries
Esko Nuutila (1995)
Efficient transitive closure computation in large digraphs, 74
Alan Frisch, Christopher Jefferson, B. Hernández, Ian Miguel (2005)
The Rules of Constraint Modelling
J. Puget (2005)
Breaking symmetries in all different problems
Variable symmetries in a constraint satisfaction problem can be broken by adding lexicographic ordering constraints. Existing general methods of generating such sets of ordering constraints can require a huge number of constraints. This adds an unacceptable overhead to the solving process. Methods exist by which this large set of ordering constraints can be reduced to a much smaller set automatically, but their application is also prohibitively costly. In contrast, this paper takes a bottom-up approach. It examines some commonly-occurring families of groups and derives a minimal set of ordering constraints sufficient to break the symmetry each group describes. These minimal sets are then used as building blocks to generate minimal sets of ordering constraints for groups constructed via direct and imprimitive wreath products. Experimental results confirm the value of minimal sets of ordering constraints, which can now be generated much more cheaply than with previous methods.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Mar 3, 2010
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