Graph Coloring Problem Based on Learning Automata

The vertex coloring problem is a well-known classical problem in graph theory in which a color is assigned to each vertex of the graph such that no two adjacent vertices have the same color. The minimum vertex coloring problem is known to be an NP-hard problem in an arbitrary graph, and a host of approximation solutions are available. In this paper, four learning automata-based approximation algorithms are proposed for solving the minimum (vertex) coloring problem. It is shown that by a proper choice of the parameters of the algorithm, the probability of approximating the optimal solution is as close to unity as possible. The last proposed algorithm is compared with some well-known coloring algorithms and the results show the efficiency of the proposed algorithm in terms of the color set size and running time of algorithm.