Finding All Stable Matchings with Assignment Constraints

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