Static and dynamic structural symmetry breaking

Authors:
Pierre Flener;Justin Pearson;Meinolf Sellmann;Pascal Van Hentenryck
Affiliations:
Dept of Information Technology, Uppsala University, Uppsala, Sweden;Dept of Information Technology, Uppsala University, Uppsala, Sweden;Dept of Computer Science, Brown University, Providence, RI;Dept of Computer Science, Brown University, Providence, RI
Venue:
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Year:
2006

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Abstract

We reconsider the idea of structural symmetry breaking (SSB) 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 these symmetries. The amount of these symmetry-breaking constraints is linear in the size of the problem, but they possibly remove a super-exponential number of symmetries on both values and variables. Moreover, static and dynamic structural symmetry breaking coincide for static variable and value orderings.