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
A new fixed point approach for stable networks and stable marriages
Journal of Computer and System Sciences
The Geometry of Fractional Stable Matchings and its Applications
Mathematics of Operations Research
Communications of the ACM
Many-to-One Stable Matching: Geometry and Fairness
Mathematics of Operations Research
Polynomial time algorithm for an optimal stable assignment with multiple partners
Theoretical Computer Science
Hardness results on the man-exchange stable marriage problem with short preference lists
Information Processing Letters
Rotations in the stable b-matching problem
Theoretical Computer Science
| Hi-index | 5.23 |
The hospitals/residents (HR) problem is a many-to-one generalization of the stable marriage (SM) problem. Researchers have been interested in variants of stable matchings that either satisfy a set of additional contraints or are optimal with respect to some cost function. In this paper, we show that broad classes of feasibility and optimization stable matching problems in the HR setting can be solved efficiently provided certain tasks (such as checking the feasibility of a stable matching or computing the cost of a stable matching) can also be done efficiently. To prove our results, we make use of an HR instance's meta-rotation poset to explore its stable matchings. An algorithm that can discover all the meta-rotations of the instance serves as a starting point for all our algorithms.