Near-Feasible Stable Matchings with Couples
针对带伴侣的住院医师匹配问题中稳定匹配可能不存在的情况，证明通过微调医院容量（总容量最多增加4，每家医院最多调整2）总能得到一个有稳定匹配的邻近实例。
The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a “nearby” instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two.