邀请嘉宾： 韩旭 清华大学计算机系17级博士研究生，来自清华大学自然语言处理组，由刘知远副教授指导，主要研究方向为自然语言处理及信息抽取。目前已在人工智能、自然语言处理等领域的著名国际会议ACL，EMNLP，NAACL，COLING，AAAI发表相关论文多篇，在Github上维护开源工程多项。
We introduce a variant of the three-sided stable matching problem for a PhD market with students, advisors, and co-advisors. In our formalization, students have consistent (lexicographic) preferences over advisors and co-advisors, and the latter have preferences over students only (hence advisors and co-advisors are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and student-co-advisor pairs may not be mutually acceptable, e.g., a student may not want to work with an advisor or co-advisor and vice versa. We show that stable three-sided matchings always exist, and present the PhD algorithm, a three-sided matching algorithm with polynomial running time which uses any two-sided stable matching algorithm as matching engine. Borrowing from results on two-sided markets, we provide some approximate optimality results. We also present an extension to three-sided markets with quotas, where each student conducts several projects, and each project is supervised by one advisor and one co-advisor. As it is often the case in practice that the same student should not do more than one project with the same advisor or co-advisor, we modify our PhD algorithm for this setting by adapting the two-sided Gale--Shapley algorithm to many-to-many two-sided markets, in which the same pair can match at most once. We also generalize the three-sided market to an $n$-sided market consisting of $n-1$ two-sided markets. We extend the PhD algorithm to this multi-sided setting to compute a stable matching in polynomial time, and we discuss its extension to arbitrary quotas. Finally, we illustrate the challenges that arise when not all advisor-co-advisor pairs are compatible, and critically review the statements from [30, 29].