Model Restarts for Structural Symmetry Breaking

Daniel S. Heller, Aurojit Panda, Meinolf Sellmann, Justin Yip

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].