Graph-Based Course Scheduling Using the Malatya Vertex Coloring Algorithm for Constraint Optimization

Abstract

The course timetabling problem is a significant combinatorial optimization problem that has attracted the attention of researchers since the second half of the 20th century. Traditionally managed through manual methods, the scheduling process is time-consuming, challenging, and prone to errors. Therefore, with technological advancements, various algorithms have been developed to offer more efficient and faster solutions. In this study, the "MVC Algorithm" is applied to the course timetabling problem. The algorithm operates in two main steps: first, the Malatya Centrality(MC) values of the nodes in the timetable graph are calculated; then, the node with the highest centrality is selected and labeled with an appropriate color. Throughout the process, the main objective is to minimize course conflicts and to generate a valid timetable that complies with defined constraints. The MVC Algorithm stands out with its predictability of procedural steps and its potential to operate in polynomial time, thus offering an effective alternative to classical and heuristic methods proposed in the literature.