Student-Project Allocation with preferences over Projects

Abstract

We study the problem of allocating students to projects, where both students and lecturers have preferences over projects, and both projects and lecturers have capacities. In this context we seek a stable matching of students to projects, which respects these preference and capacity constraints. Here, the stability definition generalises the corresponding notion in the context of the classical Hospitals/Residents problem. We show that stable matchings can have different sizes, which motivates max-spa-p, the problem of finding maximum cardinality stable matching. We prove that max-spa-p is NP-hard and not approximable within δ, for some δ > 1, unless P = NP. On the other hand, we give an approximation algorithm with a performance guarantee of 2 for max-spa-p.

A Multi-Objective Approach for the Project Allocation Problem

“…Moreover, in [5] the system matches students having preferences over projects along with the lecturers having preferences over students. Students are first matched to the best project that he could obtain.…”

A Visual Implementation of Student Project Allocation

“…Lecturers' preferences offers offers Manlove and O'Malley [2] presented a model for the student project allocation with preference lists over projects denoted SPA-P. Figure2 shows an instance of the SPA-P model, the students supply preference lists over projects, while the lecturers indicate their preferences for the projects.…”

“…The algorithm is for a version of the problem in which each applicant has an associated weight. The authors in [1,2] notes A Visual Implementation of Student Project Allocation Mahmoud I. Moussa and Ahmed H. Abu El-Atta that a new model over (student, project) pairs may improve the results of the problem. This paper presents a new data structure for the student project allocation problem with preference lists over (student, project) pairs that we denote SPA-(s, p) to reduce the space that needed to present an instance of SPA-(s, p).…”

“…This instance has two stable matching M s , p s , p and M s , p s , p . It is clearly that M is better than M but in that model it is NP problem to find best matching, the authors of SPA-p models [2] note that a new model over pairs may solve that problem. In SPA-(s, p) model; The stability can be defined as the following: a stable matching M guarantees that there is no pair s , p M where l is the lecturer who offers , such that is unassigned or prefers to remain within assignment in and also is undersubscribed or prefers , to the worst pair , in .…”

Course Opening, Assignment and Timetabling with Student Preferences

“…Methods for solving the SPA problem are, among others, building an integer program and solving it with a solver Anwar and Bahaj (2003), defining a linear program for some particular cases Saber and Ghosh (2001), or developing specific heuristics like a genetic algorithm Harper et al (2005). Manlove and O'Malley Manlove and O'Malley (2008) show the complexity and give an approximation algorithm for a generalized SPA problem in which both the students and the lecturers have preferences over the projects. The main difference between the SPA problem and our case study is that in the SPA problem there is no restriction on the minimum number of students assigned to a project.…”