Minimal Envy Matchings in the Hospitals/Residents Problem with Lower Quotas
Abstract
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. Envyfreeness is introduced as a relaxation of stability that allows blocking pairs involving a resident and an empty position of a hospital. While, envyfree matching might not exist either when lower quotas are introduced. We consider the problem of finding a feasible matching that satisfies lower quotas and upper quotas and minimizes envy in terms of envypairs and envyresidents in the Hospitals/Resident problem with Lower Quota. We show that the problem is NPhard with both envy measurement. We also give a simple exponentialtime algorithm for the MinimumEnvyPair HRLQ problem.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.15559
 Bibcode:
 2021arXiv211015559H
 Keywords:

 Computer Science  Computer Science and Game Theory