Legal Assignments and Fast EADAM with Consent via Classic Theory of Stable Matchings

Since the seminal work of Gale and Shapley, stable assignments have received widespread attention for their mathematical elegance and broad applicability. However, in applications such as the school choice problem, in which public schools are often perceived as commodities and only students’ welfare matters, enforcing stability implies a loss of efficiency for the students. In “Legal assignments and fast EADAM with consent via classical theory of stable matchings,” Faenza and Zhang study two extensions of the traditional model—legal assignments and efficiency adjusted deferred acceptance mechanism (EADAM)—that strive to regain this loss in efficiency. The authors establish a tight connection between legal and stable assignments, which allows them to use critical structural tools of stable matchings, such as the concept of rotations, to design provably fast algorithms for (1) optimizing linear functions over the set of legal assignments and (2) finding the outcome of EADAM. These algorithmic results greatly improve the applicability of both extensions as witnessed by a complexity analysis and experimental results.