Posting Static Symmetry Breaking Constraints Dynamically

Symmetry is an important feature of many combinatorial search problems. We propose a new method for dynamically posting static symmetry breaking constraints during search. This method is based on the observations that any symmetry of a set of symmetry breaking constraints can be used to break symmetry, and different symmetries pick out different solutions. We choose which symmetry to post as branching decisions force the choice. Unlike other dynamic methods, we are not restricted to breaking symmetry with lexicographical ordering constraints. We prove that our method is correct and only eliminates symmetric solutions. We also identify some common conditions under which it eliminates all symmetric solutions. This approach inherits good properties of both dynamic and static symmetry breaking methods: we can have fast propagation on the posted symmetry breaking constraints without conflicting with the branching heuristic. Experimental results show that the method performs well.