Consider a set of doctors $D$ and hospitals $H$ such that each doctor $d \in D$ has a rank ordered strict preference over a subset of hospitals, $H_d \subseteq H$. Similarly, each hospital $h \in H$ has a strict rank ordered preference over a subset of the candidates, $D_h \subseteq D$. That is, the doctors and residents want to remain unmatched rather than be matched to someone who is not in their preference list. Further, each hospital $h \in H$ may have multiple identical positions, $k_h \geq 1$. That is, the doctors have no preference over the
Can the Gale-Shapley algorithm be modified to accommodate this extension naturally?