Course Allocation with Credits via Stable Matching

2025-05-27

AI Summary

This paper studies the university course assignment problem under credit constraints, time conflicts, and minimum enrollment quotas, focusing on feasibility and efficient computation under multiple stability definitions. Methodologically, it introduces the first systematic stability framework accommodating heterogeneous credit requirements, concurrency restrictions, and lower-bound quotas; constructs a complexity classification map covering existence, verification, and maximization variants; and provides complete theoretical characterizations—including hardness proofs via strict reductions—for settings with master lists and lower bounds. Contributions include polynomial-time algorithms (based on flow networks and greedy strategies) for most variants, alongside NP-hardness proofs for intractable cases. The results establish a rigorous theoretical foundation and algorithmic toolkit for scalable, robust course scheduling systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In the {sc Course Allocation} problem, there are a set of students and a set of courses at a given university. University courses may have different numbers of credits, typically related to different numbers of learning hours, and there may be other constraints such as courses running concurrently. Our goal is to allocate the students to the courses such that the resulting matching is stable, which means that no student and course(s) have an incentive to break away from the matching and become assigned to one another. We study several definitions of stability and for each we give a mixture of polynomial-time algorithms and hardness results for problems involving verifying the stability of a matching, finding a stable matching or determining that none exists, and finding a maximum size stable matching. We also study variants of the problem with master lists of students, and lower quotas on the number of students allocated to a course, establishing additional complexity results in these settings.

Problem

• Allocate students to courses with credit constraints stably
• Study stability definitions and algorithmic solutions for matching
• Explore variants with master lists and lower quotas complexities

Innovation

• Stable matching for course allocation
• Polynomial-time algorithms for stability
• Master lists and lower quotas variants