Annals of Mathematics and Artificial Intelligence

, Volume 57, Issue 1, pp 37–57

Static and dynamic structural symmetry breaking

Authors

    • Faculty of Engineering and Natural SciencesSabancı University
    • Department of Information TechnologyUppsala University
  • Justin Pearson
    • Department of Information TechnologyUppsala University
  • Meinolf Sellmann
    • Department of Computer ScienceBrown University
Article

DOI: 10.1007/s10472-009-9172-3

Cite this article as:
Flener, P., Pearson, J. & Sellmann, M. Ann Math Artif Intell (2009) 57: 37. doi:10.1007/s10472-009-9172-3

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.

Keywords

SymmetrySymmetry breakingStatic, dynamic, and structural symmetry breakingConstraint satisfaction problemWreath product

Mathematics Subject Classifications (2000)

68T2090C2705A15

Copyright information

© Springer Science+Business Media B.V. 2009