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We study a variant of the StudentProject Allocation problem with lectur...
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Capacity Expansion in the College Admission Problem
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A near Pareto optimal approach to studentsupervisor allocation with two sided preferences and workload balance
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An Integer Programming Approach to the StudentProject Allocation Problem with Preferences over Projects
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Superstability in the StudentProject Allocation Problem with Ties
The StudentProject Allocation problem with lecturer preferences over Students (SPAS) 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 preference lists are strictly ordered. Here, we study a generalisation of SPAS where ties are allowed in the preference lists of students and lecturers, which we refer to as the StudentProject Allocation problem with lecturer preferences over Students with Ties (SPAST). We investigate stable matchings under the most robust definition of stability in this context, namely superstability. We describe the first polynomialtime algorithm to find a superstable matching or to report that no such matching exists, given an instance of SPAST. 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 lineartime algorithm based on randomlygenerated SPAST instances. Our main finding is that, whilst superstable matchings can be elusive, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers' preference lists.
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