An Algorithm for Strong Stability in the Student-Project Allocation Problem with Ties
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We study a variant of the Student-Project Allocation problem with lecturer preferences over Students where ties are allowed in the preference lists of students and lecturers (SPA-ST). We investigate the concept of strong stability in this context. Informally, a matching is strongly stable if there is no student and lecturer l such that if they decide to form a private arrangement outside of the matching via one of l's proposed projects, then neither party would be worse off and at least one of them would strictly improve. We describe the first polynomial-time algorithm to find a strongly stable matching or to report that no such matching exists, given an instance of SPA-ST. Our algorithm runs in O(m^2) time, where m is the total length of the students' preference lists.
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