A unified approach to finding good stable matchings in the hospitals/residents setting

• Published in: Theoretical computer science Vol. 400; no. 1; pp. 84 - 99
• Main Authors: Cheng, Christine, McDermid, Eric, Suzuki, Ichiro
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 09.06.2008; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Calculus of variations and optimal control; College admissions problem; Computer science; control theory; systems; Exact sciences and technology; Matching hospitals to residents; Mathematical analysis; Mathematics; Meta-rotation poset; Miscellaneous; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Sciences and techniques of general use; Stable matchings; Theoretical computing; Meta-rotation poset; College admissions problem; Matching hospitals to residents; Stable matchings; Costs; Computer theory; Optimization method; Computing; Algorithm; Rotation; Optimization; Partially ordered set; Cost function; Feasibility; Marriage
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2008.02.014

The hospitals/residents (HR) problem is a many-to-one generalization of the stable marriage (SM) problem. Researchers have been interested in variants of stable matchings that either satisfy a set of additional contraints or are optimal with respect to some cost function. In this paper, we show that broad classes of feasibility and optimization stable matching problems in the HR setting can be solved efficiently provided certain tasks (such as checking the feasibility of a stable matching or computing the cost of a stable matching) can also be done efficiently. To prove our results, we make use of an HR instance’s meta-rotation poset to explore its stable matchings. An algorithm that can discover all the meta-rotations of the instance serves as a starting point for all our algorithms.