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

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