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
Hard variants of stable marriage
Theoretical Computer Science
The structure of stable marriage with indifference
Discrete Applied Mathematics
The Hospitals/Residents Problem with Ties
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Stable Marriage with Incomplete Lists and Ties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Matching Medical Students to Pairs of Hospitals: A New Variation on a Well-Known Theme
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Algorithms (TALG)
Two algorithms for the Student-Project Allocation problem
Journal of Discrete Algorithms
Strongly stable matchings in time O(nm) and extension to the hospitals-residents problem
ACM Transactions on Algorithms (TALG)
Improved approximation results for the stable marriage problem
ACM Transactions on Algorithms (TALG)
Efficient algorithms for generalized Stable Marriage and Roommates problems
Theoretical Computer Science
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The stable marriage problem with master preference lists
Discrete Applied Mathematics
Optimal matching between spatial datasets under capacity constraints
ACM Transactions on Database Systems (TODS)
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
A (2 - c1/√N)-approximation algorithm for the stable marriage problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Two-sided matching with partial information
Proceedings of the fourteenth ACM conference on Electronic commerce
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We study a version of the well-known Hospitals/Residents problem in which participants' preferences may involve ties or other forms of indifference. In this context, we investigate the concept of strong stability, arguing that this may be the most appropriate and desirable form of stability in many practical situations. When the indifference is in the form of ties, we describe an O(a2) algorithm to find a strongly stable matching, if one exists, where a is the number of mutually acceptable resident-hospital pairs. We also show a lower bound in this case in terms of the complexity of determining whether a bipartite graph contains a perfect matching. By way of contrast, we prove that it becomes NP-complete to determine whether a strongly stable matching exists if the preferences are allowed to be arbitrary partial orders.