Symmetry Breaking in Constraint Satisfaction Problems

Abstract

Abstract. Two methods performing Symmetry Breaking During Search (SBDS) are presented, as described in [1] and [2]. The first was also the the one that defined SBDS, under the name Symmetry Excluding Search, being the first attempt to use it for symmetries of arbitrary type, in contrast to previous attempts that could only handle certain symmetry types. The basic characteristic is that SBDS does not affect the search procedure, meaning that it does not force it to use paths with a certain order. The method was refined later in [2]. While in [1] mathematical proofs were given in order to obtain the final results, in [2], the use of group theory and the known properties of symmetric groups make the method more compact. Moreover, in the first case the authors had to implement their method by writing explicit code for everything, while in the second case, a combination of two systems, ECL i PS e and GAP, is used, which results in formalizing the use of symmetries, making the separation between the search procedure and symmetry breaking more clear. In addition, the method becomes now easier to use, since the programmer no longer needs to keep in mind how symmetries work. GAP provides all the information needed, leaving the programmer with the need only to implement the search procedure, using directly the results for symmetry exclusion given by GAP. Examples and experimental results are provided for both cases, indicating the significant profit in reducing the search space, and thus search time in solving Constraint Satisfaction Problems.