Combinatorial theory (2nd ed.)
Combinatorial theory (2nd ed.)
Kirkman triple systems of order 21 with nontrivial automorphism group
Mathematics of Computation
Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
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
Scheduling social tournaments locally
AI Communications - Constraint Programming for Planning and Scheduling
Scheduling social golfers with memetic evolutionary programming
HM'06 Proceedings of the Third international conference on Hybrid Metaheuristics
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The Social Golfer Problem has been extensively used by the constraint community in recent years as an example of a highly symmetric 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 Kirkman驴s Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, a generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques improves previously published results by an order of magnitude for CPU time as well as for number of backtracks. It computes the seven unique solutions of Kirkman驴s problem in a few seconds.