Stable Matchings with Ties, Master Preference Lists, and Matroid Constraints

In this paper, we consider a matroid generalization of the hospitals/residents problem with ties and master lists. In this model, the capacity constraints for hospitals are generalized to matroid constraints. By generalizing the algorithms of O'Malley for the hospitals/residents problem with ties and master lists, we give polynomial-time algorithms for deciding whether there exist a super-stable matching and a strongly stable matching in our model, and finding such matchings if they exist.