The complexity of counting stable marriages
SIAM Journal on Computing
Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
The set of super-stable marriages forms a distributive lattice
Discrete Applied Mathematics
Preference structures and their numerical representations
Theoretical Computer Science
Hard variants of stable marriage
Theoretical Computer Science
Strong Stability in the Hospitals/Residents Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Efficient algorithms for generalized Stable Marriage and Roommates problems
Theoretical Computer Science
Weights in stable marriage problems increase manipulation opportunities
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Two-sided matching with partial information
Proceedings of the fourteenth ACM conference on Electronic commerce
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We consider the stable marriage problem where participants are permitted to express indifference in their preference lists (i.e., each list can be partially ordered). We prove that, in an instance where indifference takes the form of ties, the set of strongly stable matchings forms a distributive lattice. However, we show that this lattice structure may be absent if indifference is in the form of arbitrary partial orders. Also, for a given stable marriage instance with ties, we characterise strongly stable matchings in terms of perfect matchings in bipartite graphs. Finally, we briefly outline an alternative proof of the known result that, in a stable marriage instance with indifference in the form of arbitrary partial orders, the set of super-stable matchings forms a distributive lattice.