The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Lower bounds for the stable marriage problem and its variants
SIAM Journal on Computing
NP-complete stable matching problems
Journal of Algorithms
Three-dimensional stable matching problems
SIAM Journal on Discrete Mathematics
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Hard variants of stable marriage
Theoretical Computer Science
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
Propagation algorithms for lexicographic ordering constraints
Artificial Intelligence
Domain permutation reduction for constraint satisfaction problems
Artificial Intelligence
A Constraint Programming Approach to the Hospitals / Residents Problem
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Propagation algorithms for lexicographic ordering constraints
Artificial Intelligence
Constraint models for graceful graphs
Constraints
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Infinite order Lorenz dominance for fair multiagent optimization
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Distributed stable matching problems with ties and incomplete lists
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
A specialised binary constraint for the stable marriage problem
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem
INFORMS Journal on Computing
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The Stable Marriage problem (SM) is an extensively-studied combinatorial problem with many practical applications. In this paper we present two encodings of an instance I of SM as an instance J of a Constraint Satisfaction Problem. We prove that, in a precise sense, establishing arc consistency in J is equivalent to the action of the established Extended Gale/Shapley algorithm for SM on I. As a consequence of this, the man-optimal and woman-optimal stable matchings can be derived immediately. Furthermore we show that, in both encodings, all solutions of I may be enumerated in a failure-free manner. Our results indicate the applicability of Constraint Programming to the domain of stable matching problems in general, many of which are NP-hard.