A fuzzy irregular cellular automata-based method for the vertex colouring problem. Issue 1 (2nd January 2020) - Kashani, Mostafa; Gorgin, Saeid; Shojaedini, Seyed Vahab
ABSTRACT: Vertex colouring is among the most important problems in graph theory which has been widely applied across different real-world problems. In vertex colouring problem (VCP), the goal is to assign a distinct colour to each vertex of the graph in such a way that no two adjacent vertices have the same colour. This paper presents a fuzzy irregular cellular automaton (FICA) for finding a near-optimal solution for the VCP. FICA is an extension fuzzy cellular automaton (FCA) in which the cells of the automaton can be arranged in an irregular structure. The aim of the proposed method is to reap the benefits of both FCA and irregular cellular automata while minimising their drawbacks. To evaluate the proposed method, various computer simulations have been conducted on a variety of graphs. The results suggest that the proposed method is able to achieve better results in terms of the minimum number of required colours and the execution time of the algorithm, compared to other peer algorithms.