Static and Dynamic Structural Symmetry Breaking

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