Finding All Stable Matchings with Assignment Constraints

In this paper we consider stable matchings that are subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm that determines when assignment constraints are compatible with stability. Whenever a stable matching consistent with the assignment constraints exists, our algorithm will output all of them (in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings with assignment constraints, and (ii) a separate tool to implement them