Finding all stable matchings with assignment constraints
提出一种算法，用于判断给定分配约束是否与稳定性兼容，并在可行时输出所有满足约束的稳定匹配，为市场设计者提供可行性测试和实施工具。
In this paper we consider stable matchings 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, based on the iterated deletion of unattractive alternatives ( Balinski and Ratier, 1997 ; Gutin et al., 2023 ), that determines if and when a given list of constraints is compatible with stability. Whenever there is a stable matching that satisfies the constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.