A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Solving difficult SAT instances in the presence of symmetry
Proceedings of the 39th annual Design Automation Conference
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Constraint Models for the Covering Test Problem
Constraints
Model Restarts for Structural Symmetry Breaking
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Combining Symmetry Breaking and Global Constraints
Recent Advances in Constraints
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Breaking symmetries in all different problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Snake lex: an alternative to double lex
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Minimal ordering constraints for some families of variable symmetries
Annals of Mathematics and Artificial Intelligence
Symmetries of Symmetry Breaking Constraints
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
On the complexity and completeness of static constraints for breaking row and column symmetry
CP'10 Proceedings of the 16th 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
Automatic generation of constraints for partial symmetry breaking
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Static and dynamic structural symmetry breaking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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Breaking the exponential number of all symmetries of a constraint satisfaction problem is often too costly. In practice, we often aim at breaking a subset of the symmetries efficiently, which we call target symmetries. In static symmetry breaking, the goal is to post a set of constraints to break these target symmetries in order to reduce the solution set and thus also the search space. Symmetries of a problem are all intertwined. A symmetry breaking constraint intended for a particular symmetry almost always breaks more than just the intended symmetry as a side-effect. Different constraints for breaking the same target symmetry can have different side-effects. Conventional wisdom suggests that we should select a symmetry breaking constraint that has more side-effects by breaking more symmetries. While this wisdom is valid in many ways, we should be careful where the side-effects take place. A symmetry σ of a CSP $\mathcal{P} = (\mathcal{V},\mathcal{D},\mathcal{C})$ is preserved by a set of symmetry breaking constraints Csb iff σ is a symmetry of $\mathcal{P}' = (\mathcal{V},\mathcal{D},\mathcal{C} \cup C^{sb})$. We give theorems and examples to demonstrate that it is beneficial to post symmetry breaking constraints that preserve the target symmetries and restrict the side-effects to only non-target symmetries as much as possible. The benefits are in terms of the number of symmetries broken and the extent to which a symmetry is broken (or eliminated), resulting in a smaller solution set and search space. Extensive experiments are also conducted to confirm the feasibility and efficiency of our proposal empirically.