Heuristic methods to determine the rainbow connectivity of a graph

• Main Authors: Jian-Yi He, 何建毅
• Other Authors: Wen-Yu Chung
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/42229136466344243077

碩士 === 國立高雄應用科技大學 === 資訊工程系 === 103 === Let G be an edge-colored graph. If G has non-repetitive colors on at least one path between any two distinct nodes, G is called rainbow connected. We used Genetic Algorithm to find the smallest possible rainbow connection colors. Using graph characteristics, we developed a heuristic method to search quickly for rainbow connected paths, and to determine whether G is rainbow connected. We also limit the minimum number of colors in the paths. The latter is named k’-constraint rainbow connection. The method essentially follows the branch-and-bound approach, which generates a path tree and prunes unnecessary branches (invalid paths). We included several specific graphs as well as random graphs to investigate the feasibility of our method. Results showed that our approach is faster and the search focused on valid paths. We hope the understanding of the relation between graph topology and edge coloring will contribute to design rainbow coloring of generic graphs in the future.