Symmetry Breaking Using Stabilizers

The addition of symmetry breaking constraints is one of the most successful symmetry breaking technique for constraint satisfaction problems (CSP). In this paper we present STAB, a method that adds some symmetry breaking constraints during the search for solution. STAB adds constraints that are not yet broken by the current partial assignment. The computation of those additional constraints require the computation of graph isomorphism at each node. Graph isomorphism is not know to be NP complete, and in practice can be solved quite efficiently using an auxiliary CSP. The method is refined to be applied to matrix problems where rows and columns can be permuted. A theoretical comparison with previously published methods shows how to combine those methods together safely. An experimental comparison on a class of highly symmetrical combinatorial problems, namely BIBD shows that STAB is more than one order of magnitude more efficient than best published techniques so far.