Classified Stable Matching

We introduce the classified stable matching problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences over the other side. An institute classifies the applicants based on their research areas (or any other criterion), and, for each class, it sets a lower bound and an upper bound on the number of applicants it would hire in that class. The objective is to find a stable matching from which no group of participants has reason to deviate. Moreover, the matching should respect the upper/lower bounds of the classes. In the first part of the paper, we study classified stable matching problems whose classifications belong to a fixed set of "order types." We show that if the set consists entirely of downward forests, there is a polynomialtime algorithm; otherwise, it is NP-complete to decide the existence of a stable matching. In the second part, we investi...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Chien-Chung Huang
• Keywords: Classified Stable Matching, Discrete Algorithms, SODA 2010, Stable Matching Polytope, Stable Matching Problem