On Stable Matchings with Pairwise Preferences and Matroid Constraints

In this paper, we consider the following generalization of the stable matching problem. We are given a set of doctors and a set of hospitals. In the classical model, each doctor has a strict total order over the hospitals. On the other hand, in our model, each doctor has a pairwise preference over the hospitals, which was introduced by Farczadi, Georgiou, and Könemann. Roughly speaking, in a pairwise preference, transitivity does not necessarily hold, and a comparison between some hospitals is not relevant to stability. Furthermore, we generalize capacity constraints on the hospitals to matroid constraints. Especially, we focus on the situation in which we are given a master list over the doctors, and the preference list of each hospital over the doctors is derived from this master list. For this problem, we give several hardness results and polynomial-time solvable cases.