Annals of Mathematics and Artificial Intelligence

, Volume 57, Issue 1, pp 37-57

First online:

Static and dynamic structural symmetry breaking

  • Pierre FlenerAffiliated withFaculty of Engineering and Natural Sciences, Sabancı UniversityDepartment of Information Technology, Uppsala University Email author 
  • , Justin PearsonAffiliated withDepartment of Information Technology, Uppsala University
  • , Meinolf SellmannAffiliated withDepartment of Computer Science, Brown University

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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.


Symmetry Symmetry breaking Static, dynamic, and structural symmetry breaking Constraint satisfaction problem Wreath product

Mathematics Subject Classifications (2000)

68T20 90C27 05A15