Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties

@article{Goko2021MaximallySL,
  title={Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties},
  author={Hiromichi Goko and Kazuhisa Makino and S. Miyazaki and Yu Yokoi},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.03093}
}
Motivated by the serious problem that hospitals in rural areas suffer from a shortage of residents, we study the Hospitals/Residents model in which hospitals are associated with lower quotas and the objective is to satisfy them as much as possible. When preference lists are strict, the number of residents assigned to each hospital is the same in any stable matching because of the well-known rural hospitals theorem; thus there is no room for algorithmic interventions. However, when ties are… 

Figures and Tables from this paper

Incomplete List Setting of the Hospitals/Residents Problem with Maximally Satisfying Lower Quotas

This paper studies a more general model where preference lists may be incomplete, and obtains maximum gaps of the best and worst solutions, approximability results, and inapproximable results.

A Fine-grained View on Stable Many-to-one Matching Problems with Lower and Upper Quotas

This work presents a polynomial-time algorithm that finds a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero.

Bipartite Matchings with Group Fairness and Individual Fairness Constraints

This work addresses group as well as individual fairness constraints in matchings in the context of assigning items to platforms by providing a polynomial-time algorithm that computes a probabilistic individually fair distribution over group fair matchings.

References

SHOWING 1-10 OF 69 REFERENCES

How good are Popular Matchings?

This comprehensive study reveals the practical appeal of popular matchings for the HR and HRLQ problems and proposes a simple modification to Yokoi's algorithm to output a maximal envy-free matching.

Envy-Free Matchings with Lower Quotas

It is shown that, for this model, deciding the existence of an envy-free matching is NP-hard in general, but solvable in polynomial time if quotas are paramodular.

On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets

the positions they do fill are filled by foreign medical school graduates. It has been suggested that changes in the manner in which the clearinghouse treats hospitals and students might alter this

A Fine-grained View on Stable Many-to-one Matching Problems with Lower and Upper Quotas

This work presents a polynomial-time algorithm that finds a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero.

The Hospitals/Residents Problem with Ties

This work presents the first linear-time algorithm for the hospitals/ residents problem under the strongest of these criteria, so-called super-stability, which has applications to large-scale matching schemes, such as the National Resident Matching Program in the US and similar schemes elsewhere.

A Matroid Approach to Stable Matchings with Lower Quotas

A matroid-based approach to the laminar classified stable matching problem (LCSM) is proposed and it is proved that the set of stable assignments of the LCSM problem has a lattice structure similarly to the ordinary stable matching model.

Strategyproof Matching with Minimum Quotas

Two new classes of strategyproof mechanisms are introduced that allow for minimum quotas as an explicit input and are argued to improve the performance of matching markets with minimum quota constraints in practice.

Stable Matchings with Ties, Master Preference Lists, and Matroid Constraints

A matroid generalization of the hospitals/residents problem with ties and master lists is considered, and polynomial-time algorithms for deciding whether there exist a super-stable matching and a strongly stable matching in this model are given.

Linear Time Local Approximation Algorithm for Maximum Stable Marriage

A two-sided market under incomplete preference lists with ties, where the goal is to find a maximum size stable matching, is considered, and a very natural, economically reasonable, local, linear time algorithm is presented.
...