Independent Sets Extraction Graph Coloring Algorithm Using Beam Search

Abstract

The graph coloring problem is an important problem with many known applications, but it is not realistic to apply the exact algorithms to large graphs. Therefore, heuristics are used in many cases. RLF has been reported to obtain better quality solutions for many instances than other greedy algorithms, and many derivatives of RLF have been proposed. RLF first chooses the vertex with the largest degree among the uncolored vertices, and then colors it. After that, RLF colors the given graph by iteratively extracting the maximum independent set of vertices based on the vertex. In this paper, we propose an algorithm that improves RLF. The proposed method applies beam search to the part of RLF that chooses the vertex with the largest degree, and obtains a better quality solution than RLF. Furthermore, the parallelization of the program suppresses the increase in computation time due to beam search. Computer experiments using the benchmark problem showed that the proposed method improves the quality of the solution by about 30% with a time increase of several times compared to RLF.