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.

讲师优先于学生（spa-s）的学生项目分配问题涉及根据学生对项目的偏爱，讲师对学生的偏爱以及每个项目和讲师可容纳的最大学生数来分配学生到项目。这个经典模型假设每个项目都是由一名讲师提供的，并且偏好列表是严格排序的。在这里，我们研究了spa-s的一般化，其中允许在学生和讲师的偏好列表中建立联系，我们将其称为与讲师的学生相比，讲师偏好的学生项目分配问题（spa-st）。在这种情况下，我们会根据最稳定的稳定性定义来研究稳定匹配，即超级稳定性。我们描述了第一个多项式时间算法，以找到超稳定匹配或报告给定spa-st实例不存在这样的匹配。我们的算法以O（L）时间运行，其中L是所有首选项列表的总长度。最后，我们介绍了基于随机生成的spa-st的线性时间算法的经验评估所获得的结果实例。我们的主要发现是，尽管在学生和讲师的偏好列表中存在联系时，超稳定匹配可能难以捉摸，但如果将联系限制在讲师的偏好列表中，则存在这种匹配的可能性就会大大提高。