# Minimal Envy Matchings in the Hospitals/Residents Problem with Lower Quotas

@article{Hu2021MinimalEM, title={Minimal Envy Matchings in the Hospitals/Residents Problem with Lower Quotas}, author={Changyong Hu and Vijay Kumar Garg}, journal={ArXiv}, year={2021}, volume={abs/2110.15559} }

In the Hospitals/Residents problem, every hospital has an upper quota that limits the number of residents assigned to it. While, in some applications, each hospital also has a lower quota for the number of residents it receives. In this setting, a stable matching may not exist. Envy-freeness is introduced as a relaxation of stability that allows blocking pairs involving a resident and an empty position of a hospital. While, envy-free matching might not exist either when lower quotas are…

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## References

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