Dynamic Posting of Static Symmetry Breaking Constraints∗

We have proposed a method for dynamically posting symmetry breaking constraints to eliminate value interchangeability [1]. We now extend this method to work with any type of symmetry breaking constraint for any type of symmetry. We prove that this method is correct in general. That is, it only eliminates symmetric solutions. We also identify some simple conditions when it eliminates all symmetric solutions. We illustrate the method with a common type of symmetry where both variables and values partition into interchangeable sets, and a polynomial number of symmetry breaking constraints breaks an exponential number of symmetries. This hybrid approach inherits good properties of both dynamic and static symmetry breaking methods: we can have fast and efficient propagation on the posted symmetry breaking constraints, yet we do not conflict with the branching heuristic.