Exploiting Single-Cycle Symmetries in Continuous Constraint Problems
This work addresses a niche problem for researchers in continuous constraint solving, offering an incremental improvement by extending symmetry exploitation from discrete to continuous domains.
The paper tackles the under-explored issue of symmetries in continuous constraint problems by focusing on single-cycle permutations, proposing a procedure that interacts with solvers without interference and quantifies symmetric box classes as a function of dimensionality. It demonstrates performance on problems like the cyclic n-roots, though concrete numerical results are not provided in the abstract.
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.