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Super-stability in the student-project allocation problem with ties

Author

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  • Sofiat Olaosebikan

    (University of Glasgow)

  • David Manlove

    (University of Glasgow)

Abstract

The Student-Project Allocation problem with lecturer preferences over Students (spa-s) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of students that each project and lecturer can accommodate. This classical model assumes that each project is offered by one lecturer and that preference lists are strictly ordered. Here, we study a generalisation of spa-s where ties are allowed in the preference lists of students and lecturers, which we refer to as the Student-Project Allocation problem with lecturer preferences over Students with Ties (spa-st). We investigate stable matchings under the most robust definition of stability in this context, namely super-stability. We describe the first polynomial-time algorithm to find a super-stable matching or to report that no such matching exists, given an instance of spa-st. Our algorithm runs in O(L) time, where L is the total length of all the preference lists. Finally, we present results obtained from an empirical evaluation of the linear-time algorithm based on randomly-generated spa-st instances. Our main finding is that, whilst super-stable matchings can be elusive when ties are present in the students’ and lecturers’ preference lists, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers’ preference lists.

Suggested Citation

  • Sofiat Olaosebikan & David Manlove, 2022. "Super-stability in the student-project allocation problem with ties," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1203-1239, July.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:5:d:10.1007_s10878-020-00632-x
    DOI: 10.1007/s10878-020-00632-x
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    References listed on IDEAS

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    1. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    2. Marco Chiarandini & Rolf Fagerberg & Stefano Gualandi, 2019. "Handling preferences in student-project allocation," Annals of Operations Research, Springer, vol. 275(1), pages 39-78, April.
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    Cited by:

    1. Naoyuki Kamiyama, 2022. "Strongly Stable Matchings under Matroid Constraints," Papers 2208.11272, arXiv.org, revised Sep 2022.

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