Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Static and dynamic structural symmetry breaking

Static and dynamic structural symmetry breaking We reconsider the idea of structural symmetry breaking for constraint satisfaction problems (CSPs). We show that the dynamic dominance checks used in symmetry breaking by dominance-detection search for CSPs with piecewise variable and value symmetries have a static counterpart: there exists a set of constraints that can be posted at the root node and that breaks all the compositions of these (unconditional) symmetries. The amount of these symmetry-breaking constraints is linear in the size of the problem, and yet they are able to remove a super-exponential number of symmetries on both values and variables. Moreover, we compare the search trees under static and dynamic structural symmetry breaking when using fixed variable and value orderings. These results are then generalised to wreath-symmetric CSPs with both variable and value symmetries. We show that there also exists a polynomial-time dominance-detection algorithm for this class of CSPs, as well as a linear-sized set of constraints that breaks these symmetries statically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Loading next page...
 
/lp/springer-journals/static-and-dynamic-structural-symmetry-breaking-1rxx18pCRC

References (28)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media B.V.
Subject
Computer Science; Statistical Physics, Dynamical Systems and Complexity; Mathematics, general; Computer Science, general; Artificial Intelligence (incl. Robotics)
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-009-9172-3
Publisher site
See Article on Publisher Site

Abstract

We reconsider the idea of structural symmetry breaking for constraint satisfaction problems (CSPs). We show that the dynamic dominance checks used in symmetry breaking by dominance-detection search for CSPs with piecewise variable and value symmetries have a static counterpart: there exists a set of constraints that can be posted at the root node and that breaks all the compositions of these (unconditional) symmetries. The amount of these symmetry-breaking constraints is linear in the size of the problem, and yet they are able to remove a super-exponential number of symmetries on both values and variables. Moreover, we compare the search trees under static and dynamic structural symmetry breaking when using fixed variable and value orderings. These results are then generalised to wreath-symmetric CSPs with both variable and value symmetries. We show that there also exists a polynomial-time dominance-detection algorithm for this class of CSPs, as well as a linear-sized set of constraints that breaks these symmetries statically.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Dec 24, 2009

There are no references for this article.