{"type":"ScholarlyArticle","title":"A Reduction based Method for Coloring Very Large Graphs","authors":[{"name":"Jinkun Lin","slug":"jinkun-lin","given":"Jinkun","family":"Lin","affiliation":"School of Electronics Engineering and Computer Science , Peking University , Beijing China; College of Information Science and Technology , Jinan University , China"},{"name":"Shaowei Cai","slug":"shaowei-cai","given":"Shaowei","family":"Cai","affiliation":"State Key Laboratory of Computer Science , Institute of Software , Chinese Academy of Sciences , China"},{"name":"Chuan Luo","slug":"chuan-luo","given":"Chuan","family":"Luo","affiliation":"Institute of Computing Technology , Chinese Academy of Sciences , China"},{"name":"Kaile Su","slug":"kaile-su","given":"Kaile","family":"Su","affiliation":"College of Information Science and Technology , Jinan University , China; Institute for Integrated and Intelligent Systems , Griffith University , Australia"}],"abstract":"The graph coloring problem (GCP) is one of the most studied NP hard problems and has numerous applications. Despite the practical importance of GCP, there are limited works in solving GCP for very large graphs. This paper explores techniques for solving GCP on very large real world graphs.We first propose a reduction rule for GCP, which is based on a novel concept called degree bounded independent set.The rule is iteratively executed by interleaving between lower bound computation and graph reduction. Based on this rule, we develop a novel method called FastColor, which also exploits fast clique and coloring heuristics. We carry out experiments to compare our method FastColor with two best algorithms for coloring large graphs we could find. Experiments on a broad range of real world large graphs show the superiority of our method. Additionally, our method maintains both upper bound and lower bound on the optimal solution, and thus it proves an optimal solution when the upper bound meets the lower bound. In our experiments, it proves the optimal solution for 97 out of 142 instances.","doi":"10.24963/ijcai.2017/73","url":"https://ijcai.org/proceedings/2017/73","pdf":"https://ijcai.org/proceedings/2017/0073.pdf","markdown":"https://ijcai.org/proceedings/2017/73.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/73","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Combinatorial & Heuristic Search","track":"Main track","number":73,"pages":{"first":517,"last":523},"keywords":["Combinatorial & Heuristic Search: Combinatorial search/optimisation","Combinatorial & Heuristic Search: Heuristic Search"],"videos":[],"references":[{"position":1,"raw":"[Batagelj and Zaversnik, 2003] Vladimir Batagelj and Mat- jaz Zaversnik. 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