Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Exploiting symmetries within constraint satisfaction search
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Groups and Constraints: Symmetry Breaking during Search
CP '02 Proceedings of the 8th 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
Constraints
A branch-and-prune solver for distance constraints
IEEE Transactions on Robotics
Exploiting single-cycle symmetries in continuous constraint problems
Journal of Artificial Intelligence Research
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As a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice.