Publication

Exploiting single-cycle symmetries in continuous constraint problems

Journal Article (2009)

Journal

Journal of Artificial Intelligence Research

Pages

499-520

Volume

34

Doc link

http://www.jair.org/media/2711/live-2711-4351-jair.pdf

File

Download the digital copy of the doc pdf document

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 field and the cyclic n-roots problem are used to show the performance of the approach in practice.

Categories

robots.

Author keywords

constraint satisfaction, continuous constraint satisfaction, symmetry, symmetric boxes, branch-and-prune

Scientific reference

V. Ruiz de Angulo and C. Torras. Exploiting single-cycle symmetries in continuous constraint problems. Journal of Artificial Intelligence Research, 34: 499-520, 2009.