Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Journal of Symbolic Computation
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
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
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Exploiting single-cycle symmetries in Branch-and-Prune algorithms
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
A branch-and-prune solver for distance constraints
IEEE Transactions on Robotics
Symmetry breaking in numeric constraint problems
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Hi-index | 0.00 |
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here 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 continuous constraint solver 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 analyze these classes and quantify them as a function of the cube dimensionality. 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 the cyclic n-roots problem are used to show the performance of the approach in practice.