Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction

Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class ...

• Type: Journal
• Year: 2006
• Where: CONSTRAINTS
• Authors: Y. Law, J. Lee
• Keywords: CONSTRAINTS 2006, Symmetries, Symmetry, Value Symmetries