Profile-based optimal matchings in the Student/Project Allocation problem

TL;DR

This paper introduces efficient algorithms for optimal student-project matchings in SPA, maximizing profile quality and accommodating additional constraints, with empirical validation of their effectiveness.

Contribution

It presents novel algorithms for greedy and generous maximum matchings in SPA, handling complex constraints through flow network techniques.

Findings

Algorithms efficiently find lexicographically maximum and minimum profiles.

The approach flexibly incorporates lecturer lower quotas.

Empirical results demonstrate practical effectiveness.

Abstract

In the Student / Project Allocation problem (SPA) we seek to assign students to individual or group projects offered by lecturers. Students provide a list of projects they find acceptable in order of preference. Each student can be assigned to at most one project and there are constraints on the maximum number of students that can be assigned to each project and lecturer. We seek matchings of students to projects that are optimal with respect to profile, which is a vector whose rth component indicates how many students have their rth-choice project. We present an efficient algorithm for finding a greedy maximum matching in the SPA context - this is a maximum matching whose profile is lexicographically maximum. We then show how to adapt this algorithm to find a generous maximum matching - this is a matching whose reverse profile is lexicographically minimum. Our algorithms involve finding optimal flows in networks. We demonstrate how this approach can allow for additional constraints, such as lecturer lower quotas, to be handled flexibly. Finally we present results obtained from an empirical evaluation of the algorithms.