Abstract
Real-world matching scenarios, like the matching of students to courses in a university setting, involve complex downward-feasible constraints like credit limits, time-slot constraints for courses, basket constraints (say, at most one humanities elective for a student), in addition to the preferences of students over courses and vice versa, and class capacities. We model this problem as a many-to-many bipartite matching problem where both students and courses specify preferences over each other and students have a set of downward-feasible constraints. We propose an Iterative Algorithm Framework that uses a many-to-one matching algorithm and outputs a many-to-many matching that satisfies all the constraints. We prove that the output of such an algorithm is Pareto-optimal from the student-side if the many-to-one algorithm used is Pareto-optimal from the student side. For a given matching, we propose a new metric called the Mean Effective Average Rank (MEAR), which quantifies the goodness of allotment from the side of the students or the courses. We empirically evaluate two many-to-one matching algorithms with synthetic data modeled on real-world instances and present the evaluation of these two algorithms on different metrics including MEAR scores, matching size and number of unstable pairs.
A. Utture—Part of this work was done when the author was a Dual Degree student at the Indian Institute of Technology Madras.
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Utture, A., Somani, V., Krishnaa, P., Nasre, M. (2019). Student Course Allocation with Constraints. In: Kotsireas, I., Pardalos, P., Parsopoulos, K., Souravlias, D., Tsokas, A. (eds) Analysis of Experimental Algorithms. SEA 2019. Lecture Notes in Computer Science(), vol 11544. Springer, Cham. https://doi.org/10.1007/978-3-030-34029-2_4
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