As a ﬁrst attempt to exploit symmetries in continuous con- straint 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.
CitationRuiz de Angulo, Vicente; Torras, Carme. "Exploiting single-cycle symmetries in branch-and-prune algorithms". 13th International Conference on Principles and Practice of Constraint Programming (CP), Providence, Estats Units d'Amèrica, 2007. A: Lecture Notes in Computer Science, vol. 4741. Berlin, Alemanya: Springer Verlag, 2007, p. 864 - 871.
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