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http://dx.doi.org/10.9708/jksci.2015.20.4.111

Chromatic Number Algorithm for Exam Scheduling Problem  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
Journal of the Korea Society of Computer and Information / v.20, no.4, 2015 , pp. 111-117 More about this Journal
Abstract
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. Gu${\acute{e}}$ret et al. tries to obtain the solution using linear programming with $O(m^4)$ 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 $B_i$ with color $C_i$ in order to exam within minimum time period and meet the incompatibility constraints. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(m) time complexity for exam scheduling problem, and gets the same solution with linear programming.
Keywords
Incompatibility; Bin packing; NP-complete; Divide-and-conquer; Chromatic number;
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