New methods to color the vertices of a graph
Communications of the ACM
Exploiting symmetries within constraint satisfaction search
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Excluding Symmetries in Constraint-Based Search
Constraints
Solving Strategies for Highly Symmetric CSPs
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Excluding Symmetries in Constraint-Based Search
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Global Cut Framework for Removing Symmetries
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Groups and Constraints: Symmetry Breaking during Search
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Global Constraints for Lexicographic Orderings
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Solving the Kirkman's Schoolgirl Problem in a Few Seconds
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Constraints
Breaking value symmetries in matrix models using channeling constraints
Proceedings of the 2005 ACM symposium on Applied computing
Using constraints to break value symmetries in constraint satisfaction problems
Using constraints to break value symmetries in constraint satisfaction problems
Removing propagation redundant constraints in redundant modeling
ACM Transactions on Computational Logic (TOCL)
The complexity of global constraints
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Efficient symmetry breaking for boolean satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Tractable symmetry breaking for CSPs with interchangeable values
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The temporal knapsack problem and its solution
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Finding Orthogonal Arrays Using Satisfiability Checkers and Symmetry Breaking Constraints
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints
INFORMS Journal on Computing
Solving Necklace Constraint Problems
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Constraint models for graceful graphs
Constraints
Breaking symmetry of interchangeable variables and values
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Evaluation of length-lex set variables
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Verification-driven slicing of UML/OCL models
Proceedings of the IEEE/ACM international conference on Automated software engineering
Symmetries of Symmetry Breaking Constraints
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Constraint programming models for graceful graphs
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
General symmetry breaking constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Increasing symmetry breaking by preserving target symmetries
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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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 of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient if-then constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals.