Stable matchings of teachers to schools

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.

Large-scale knowledge service supply and demand matching method based on subject psychology

“…The modified preference values are calculated according to (21) and (22) and shown in Table 9. According to (23) and (24), the normalized modified preference values are calculated and shown in Table 10. Establish and solve model 2.…”

“…There are also some researches on matching algorithms in other fields. For example, the matching problem between doctors and hospitals [20], the matching problem between readers and advertisers [21], the matching problem between students and universities [22], the matching problem between marriage [23], the matching problem between teachers and schools [24], and the matching problem between employees and posts [25,26]. Firstly, the matching is completed directly according to the preference information provided by the knowledge demanders (knowledge suppliers) to the knowledge suppliers (knowledge demanders).…”

Two-Sided Matching for Triangular Intuitionistic Fuzzy Numbers in Smart Environmental Protection

“…Two-sided matching has garnered much attention and has been used for a wide range of applications, such as marriage [1], advertising [2], college enrollment [3], service matching [4], teachers-schools matching [5], and so on. Now, two-sided matching has been extended to a different environment, such as ordinal numbers, order relations, and linguistic…”