Abstract
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 32. 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.
Highlights
Matching problems, which generally involve the assignment of a set of agents to another set of agents based on preferences, have wide applications in many real-world settings
We present results arising from an empirical evaluation that investigates how the solutions produced by the existing approximation algorithms for max-spa-p [11,17] compare to optimal solutions obtained from our Integer Programming (IP) model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets
The results presented suggest that even as we increase the number of students, projects, lecturers, and the length of the students’ preference lists, each of the approximation algorithms finds stable matchings that are close to Please cite this article as: D
Summary
Matching problems, which generally involve the assignment of a set of agents to another set of agents based on preferences, have wide applications in many real-world settings. We present results arising from an empirical evaluation that investigates how the solutions produced by the existing approximation algorithms for max-spa-p [11,17] compare to optimal solutions obtained from our IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. These real datasets are based on actual student preference data and manufactured lecturer preference data from previous runs of student-project allocation processes at the School of Computing Science, University of Glasgow.
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