Exploiting Single-Cycle Symmetries in Continuous Constraint Problems
  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
and#64257;eld and the cyclic n-roots problem are used to show the performance
of the approach in practice.
