Stable matchings of teachers to schools

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)

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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

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering & Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE