Cechlarova, K., Fleiner, T., Manlove, D. F. and McBride, I. (2016) Stable matchings of teachers to schools. Theoretical Computer Science, 653, pp. 15-25. (doi: 10.1016/j.tcs.2016.09.014)
|
Text
129124.pdf - Published Version Available under License Creative Commons Attribution. 385kB |
Abstract
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning teachers to schools. Our model is motivated by a particular characteristic of the education system in many countries where each teacher specializes in two subjects. We seek stable matchings, which ensure that no teacher and school have the incentive to deviate from their assignments. Indeed we propose two stability definitions depending on the precise format of schools’ preferences. If the schools’ ranking of applicants is independent of their subjects of specialism, we show that the problem of deciding whether a stable matching exists is NP-complete, even if there are only three subjects, unless there are master lists of applicants or of schools. By contrast, if the schools may order applicants differently in each of their specialization subjects, the problem of deciding whether a stable matching exists is NP-complete even in the presence of subject-specific master lists plus a master list of schools. Finally, we prove a strong inapproximability result for the problem of finding a matching with the minimum number of blocking pairs with respect to both stability definitions.
Item Type: | Articles |
---|---|
Additional Information: | Open Access funded by Engineering and Physical Sciences Research Council |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Manlove, Professor David and Cechlarova, Professor Katarina and Fleiner, Dr Tamas |
Authors: | Cechlarova, K., Fleiner, T., Manlove, D. F., and McBride, I. |
College/School: | College of Science and Engineering > School of Computing Science |
Journal Name: | Theoretical Computer Science |
Publisher: | Elsevier |
ISSN: | 0304-3975 |
ISSN (Online): | 1879-2294 |
Published Online: | 04 October 2016 |
Copyright Holders: | Copyright © 2016 The Authors |
First Published: | First published in Theoretical Computer Science 653:15-25 |
Publisher Policy: | Reproduced under a creative commons license |
University Staff: Request a correction | Enlighten Editors: Update this record