Static and dynamic structural symmetry breaking

Authors:
Pierre Flener;Justin Pearson;Meinolf Sellmann
Affiliations:
Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, Turkey 34956 and Department of Information Technology, Uppsala University, Uppsala, Sweden 751 05;Department of Information Technology, Uppsala University, Uppsala, Sweden 751 05;Department of Computer Science, Brown University, Providence, USA 02912
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2009

Citing 13
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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.