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The exam scheduling problem has been classified as nondeterministic polynomial time-complete (NP-complete) problem because of the polynomial time algorithm to obtain the exact solution has been unknown yet. Guret et al. tries to obtain the solution using linear programming with time complexity for this problem. On the other hand, this paper suggests chromatic number algorithm with O(m) time complexity. The proposed algorithm converts the original data to incompatibility matrix for modules and graph firstly. Then, this algorithm packs the minimum degree vertex (module) and not adjacent vertex to this vertex into the bin with color in order to exam within minimum time period and meet the incompatibility constraints. As a result of experiments, this algorithm reduces the of linear programming to O(m) time complexity for exam scheduling problem, and gets the same solution with linear programming.

Chromatic Number Algorithm for Exam Scheduling Problem