Exploiting Single-Cycle Symmetries in Branch-and-Prune algorithms [chapter]

Vicente Ruiz de Angulo, Carme Torras
Principles and Practice of Constraint Programming – CP 2007  
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.
more » ... 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.
doi:10.1007/978-3-540-74970-7_65 dblp:conf/cp/AnguloT07 fatcat:urfho463inet3jiqlqqtug5wui