Kirkman triple systems of order 21 with nontrivial automorphism group
Mathematics of Computation
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Global Cut Framework for Removing Symmetries
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Constraints
Removing propagation redundant constraints in redundant modeling
ACM Transactions on Computational Logic (TOCL)
Length-lex ordering for set CSPs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Tractable symmetry breaking for CSPs with interchangeable values
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
An attempt to dynamically break symmetries in the social golfers problem
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Exponential propagation for set variables
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Dynamic symmetry breaking restarted
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Set variables and local search
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Scheduling social golfers locally
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Compositional derivation of symmetries for constraint satisfaction
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
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The Social Golfer Problem has been extensivelyu sed in recent years byt he constraint communityas an example of highlysy mmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as the Kirkman's Schoolgirl Problem and list a collection of techniques and tricks to find efficientlya ll its unique solutions. In particular, we propose SBDD+, an generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques allows us to improve previous published results bya n order of magnitude for CPU time as well as number of backtracks, and to compute the seven unique solutions of the Kirkman's problem in a few seconds.