Student-project allocation with preferences over projects: Algorithmic and experimental results
| Autor: | Duncan Milne, David F. Manlove, Sofiat Olaosebikan |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Matching (statistics)
Mathematical optimization Applied Mathematics 0211 other engineering and technologies Approximation algorithm 021107 urban & regional planning Context (language use) 0102 computer and information sciences 02 engineering and technology 01 natural sciences 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Maximum size Constant (mathematics) Preference list Integer programming Mathematics |
| Zdroj: | Discrete Applied Mathematics. 308:220-234 |
| ISSN: | 0166-218X |
| Popis: | We study the Student-Project Allocation problem with lecturer preferences over Projects ( spa-p ). In this context it is known that stable matchings can have different sizes and the problem of finding a maximum size stable matching is NP-hard. There are two known approximation algorithms for max-spa-p , with performance guarantees 2 and 3 2 . We show that max-spa-p is polynomial-time solvable if there is only one lecturer involved, and NP-hard to approximate within some constant c > 1 if there are two lecturers involved. We also show that this problem remains NP-hard if each preference list is of length at most 3, with an arbitrary number of lecturers. We then describe an Integer Programming (IP) model to enable max-spa-p to be solved optimally in the general case. Following this, we present results arising from an empirical evaluation that investigates how the solutions produced by the approximation algorithms compare to optimal solutions obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect