Structural Symmetry Breaking

Symmetry breaking has been shown to be an important method to speed up the search in constraint satisfaction problems that contain symmetry. When breaking symmetry by dominance detection, a computationally efficient symmetry breaking scheme can be achieved if we can solve the dominance detection problem in polynomial time. We study the complexity of dominance detection when value and variable symmetry appear simultaneously in constraint satisfaction problems (CSPs) with single-valued variables and set-CSPs. We devise an efficient dominance detection algorithm for CSPs with single-valued variables that yields symmetry-free search trees and that is based on the abstraction to the actual, intuitive structure of a symmetric CSP.