Model Restarts for Structural Symmetry Breaking

Abstract

There exist various methods to break symmetries. The two that concern us in this paper are static symmetry breaking where we add static constraints to the problem (see e.g. [1,3]) and symmetry breaking by dominance detection (SBDD) where we filter values based on a symmetric dominance analysis when comparing the current searchnode with those that were previously expanded [2,5]. The core task of SBDD is dominance detection. The first provably polynomial-time dominance checkers for value symmetry were devised in [18] and [14]. For problems exhibiting both “piecewise” symmetric values and variables, [15] devised structural symmetry breaking (SSB). SSB is a polynomial-time dominance checker for piecewise symmetries which, used within SBDD, eliminates symmetric subproblems from the search-tree. Piecewise symmetries are of particular interest as they result naturally from symmetry detection based on a static analysis of a given CSP that exploits the knowledge about problem substructures as captured in global constraints [17]. Static SSB was developed in [4] and is based on the structural abstractions that were introduced in [17].KeywordsSymmetry BreakingConstraint Satisfaction ProblemChoice PointSymmetry DetectionDynamic Symmetry BreakingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.