Dual viewpoint heuristics for binary constraint satisfaction problems
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Artificial Intelligence
Binary vs. non-binary constraints
Artificial Intelligence
Representation Selection for Constraint Satisfaction: A Case Study Using n-Queens
IEEE Expert: Intelligent Systems and Their Applications
The Difference All-Difference Makes
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Using Auxiliary Variables and Implied Constraints to Model Non-Binary Problems
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Solving the Round Robin Problem Using Propositional Logic
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
On Forward Checking for Non-binary Constraint Satisfaction
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
CSPLIB: A Benchmark Library for Constraints
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
When do bounds and domain propagation lead to the same search space
Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming
Removing propagation redundant constraints in redundant modeling
ACM Transactions on Computational Logic (TOCL)
Duality in permutation state spaces and the dual search algorithm
Artificial Intelligence
Search in the patience game ‘Black Hole’
AI Communications - Constraint Programming for Planning and Scheduling
Solving a Stochastic Queueing Control Problem with Constraint Programming
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Scheduling with uncertain durations: Modeling β-robust scheduling with constraints
Computers and Operations Research
Guiding Search using Constraint-level Advice
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Modeling choices in quasigroup completion: SAT vs. CSP
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A constraint programming approach for solving a queueing control problem
Journal of Artificial Intelligence Research
Value ordering for finding all solutions
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Efficient SAT Techniques for Relative Encoding of Permutations with Constraints
AI '09 Proceedings of the 22nd Australasian Joint Conference on Advances in Artificial Intelligence
Constraint models for graceful graphs
Constraints
Tailoring solver-independent constraint models: a case study with ESSENCE' and MINION
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
Modelling equidistant frequency permutation arrays: an application of constraints to mathematics
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Transforming and refining abstract constraint specifications
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Speeding up weighted constraint satisfaction using redundant modeling
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
Channel and Time Slot Allocation for Dense RFID Networks
Wireless Personal Communications: An International Journal
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represemts one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combines model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combines models for two classes of problems: permutation problems and injection problems. Our results show that if often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general methodology for comparing different constraint models.