Approaches to Conditional Symmetry Breaking

Conditional symmetry arises in a sub-problem of a constraint satisfaction problem, where the sub-problem satisfies some condition under which additional symetries hold. Typically, the condition is a set of assignments of values to variables, i.e. a partial assignment reached during systematic search. Like unconditional symmetry, conditional symmetry can cause redundancy in a systematic search for solutions. Breaking this symmetry, in addition to breaking unconditional symmetry, is therefore an important part of solving a constraint satisfaction problem effectively. This paper examines three ways in which this can be done: by adding conditional symmetry-breaking constraints, by reformulating the problem to remove the symmetry, and by augmenting the search process to break the conditional symmetry dynamically.