A comparative analysis between two heuristic algorithms for the graph vertex coloring problem

This study focuses on two heuristic algorithms for the graph vertex coloring problem: the sequential (greedy) coloring algorithm (SCA) and the Welsh– Powell algorithm (WPA). The code of the algorithms is presented and discussed. The methodology and conditions of the experiments are presented. The execution time of the algorithms was calculated as the average of four different starts of the algorithms for all analyzed graphs, taking into consideration the multitasking mode of the operating system. In the graphs with less than 600 vertices, in 90% of cases, both algorithms generated the same solutions. In only 10% of cases, the WPA algorithm generates better solutions. However, in the graphs with more than 1,000 vertices, in 35% of cases, the WPA algorithm generates better solutions. The results show that the difference in the execution time of the algorithms for all graphs is acceptable, but the quality of the solutions generated by the WPA algorithm in more than 20% of cases is better compared to the SC algorithm. The results also show that the quality of the solutions is not related to the number of iterations performed by the algorithms.