The Student-Project 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 each project is offered by one lecturer and 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 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.

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.Existing results in spa-st. Every instance of spa-st admits a weakly stable matching, which could be of different sizes [21]. Moreover, the problem of finding a maximum size weakly stable matching (MAX-SPA-ST) is NP-hard [12,21], even for the so-called Stable Marriage problem with Ties and Incomplete lists (smti). Cooper and Manlove [7] described a 3 2 -approximation algorithm for MAX-SPA-ST. On the other hand, Irving et al. argued in [10] that super-stability is a natural and most robust solution concept to seek in cases where agents have incomplete information. Recently, Olaosebikan and Manlove [24] showed that if an instance of spa-st admits a superstable matching M , then all weakly stable matchings in the instance are of the same size (equal to the size of M ), and match exactly the same set of students. The main result of their paper was a polynomial-time algorithm to find a super-stable matching or report that no such matching exists, given an instance of spa-st. Their algorithm runs in O(L) time, where L is the total length of all the preference lists.Motivation. It was motivated in [11] that weakly stable matching may be undermined by bribery or persuasion, in practical applications of hrt. In what follows, we give a corresponding argument for an instance I of spa-st. Suppose that M is a weakly stable matching in I, and suppose that a student s i prefers a project p

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 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 lineartime algorithm based on randomly-generated SPA-ST instances. Our main finding is that, whilst super-stable matchings can be elusive, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers' preference lists.of HRT and applying the algorithm described in [11] to the resulting HRT instance does not work in general (we explain this further in Sect. 2.3).Our contribution. In this paper, we describe the first polynomial-time algorithm to find a superstable matching or to report that no such matching exists, given an instance of SPA-ST -thus solving an open problem given in [1,17]. Our algorithm runs in time linear in the size of the problem instance. We also present the results of an empirical evaluation based on an implementation of our linear-time algorithm that investigates how the nature of the preference lists would affect the likelihood of a superstable matching existing, with respect to randomly-generated SPA-ST instances. Our main finding is that the probability of a super-stable matching existing is significantly higher if ties are restricted to the lecturers' preference lists.The remaining sections of this paper are structured as follows. We give a formal definition of the SPA-S problem, the SPA-ST variant, and the super-stability concept in Sect. 2. We describe our algorithm for SPA-ST under super-stability in Sect. 3. Further, Sect. 3 also presents our algorithm's correctness results and some structural properties satisfied by the set of super-stable matchings in an instance of SPA-ST. In Sect. 4, we present the results of the empirical evaluation. Finally, Sect. 5 presents some concluding remarks and potential direction for future work.

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 3 2 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the 3 2 -approximation algorithm finds stable matchings that are very close to having maximum cardinality. IntroductionMatching problems, which generally involve the assignment of a set of agents to another set of agents based on preferences, have wide applications in many real-world settings. One such application can be seen in an educational context, e.g., the allocation of pupils to schools, school-leavers to universities and students to projects. In the context of allocating students to projects, university lecturers propose a range of projects, and each student is required to provide a ⋆

In this paper, we propose a hybrid beamforming architecture with constant phase shifters (CPSs) for uplink cell-free millimetre-wave (mm-Wave) massive multiple-input multiple-output (MIMO) systems based on exploiting antenna selection to reduce power consumption. However, current antenna selection techniques are applied for conventional massive MIMO, not cell-free massive MIMO systems. Therefore, the enormous computational complexity of these techniques to optimally select antennas for cell-free massive MIMO networks is caused by numerous randomly distributed access points (APs) in the service area and their large antennas. The architecture proposed in this work solves this issue by employing a low-complexity matching technique to obtain the optimal number of antennas, chosen based on channel magnitude and by switching off antennas that contribute more to interference power than to desired signal power for each radio frequency (RF) chain at each AP, instead of assuming all RF chains at each AP have the same number of selected antennas. Therefore, an assignment optimization problem based on a bipartite graph is formulated for cell-free mm-Wave massive MIMO system uplinks. Then, the Hungarian method is proposed to solve this problem due to its ability to solve this assignment problem in a polynomial time. Simulated results show that, despite several APs and antennas, the proposed matching approach is more energy-efficient and has lower computational complexity than state-of-the-art schemes.

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As computing education grows rapidly across the globe, there is an increasing need to broaden participation and engage all students in computing, particularly those from underrepresented groups and developing countries. To address this need, a programming workshop that uses various interventions to broaden participation was set up to empower African university students with computer programming skills. Out of 487 applications, 172 participants from 11 African countries were selected to participate in the workshop. This paper aims to explore the participants' experiences, including their motivation for attending the workshop, their programming skills confidence, what they found most useful for their learning, and the challenges they faced. Employing a mixed-methods design, our quantitative and qualitative results indicate that participants' motivations were more intrinsic. Further, the results indicate that participants' confidence increased after the workshop. They found the hands-on sessions with the tutors to be most beneficial to their learning. We also observed that many participants struggled with access to basic ICT resources during the workshop, even with the internet data provided for them. Our findings highlight that participants are interested in learning programming and that it is important for collaborative efforts to provide relevant teaching interventions, resources, and support for them.

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