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Static and dynamic structural symmetry breaking

Flener, Pierre and Pearson, Justin and Sellmann, Meinolf (2009) Static and dynamic structural symmetry breaking. Annals of Mathematics and Artificial Intelligence , 57 (1). pp. 37-57. ISSN 1012-2443 (Print) 1573-7470 (Online)

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Official URL: http://dx.doi.org/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.

Item Type:Article
Additional Information:Special Issue: Sp. Iss. SI
Uncontrolled Keywords:Symmetry; Symmetry breaking; Static, dynamic, and structural symmetry breaking; Constraint satisfaction problem; Wreath product
Subjects:Q Science > QA Mathematics > QA075 Electronic computers. Computer science
ID Code:13983
Deposited By:Pierre Flener
Deposited On:31 May 2010 11:27
Last Modified:25 May 2011 14:18

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