A Computational Approach to Study Ramsey Numbers

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K00307
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Intelligent informatics
• Research Institution: Kyushu University
• Principal Investigator: Fujita Hiroshi 九州大学, システム情報科学研究院, 准教授 (70284552)
• Co-Investigator(Kenkyū-buntansha): 越村 三幸 九州大学, システム情報科学研究院, 助教 (30274492)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: Ramsey number / SAT solver

Outline of Final Research Achievements

We have succeeded in finding some rare Ramsey graphs whose adjacency matrices are persymmetric, that are essential for the study of Ramsey numbers whose determination is one of the most famous and difficult problems in discrete mathematics.
For this research, it is indispensable to use various methods and problem solvers in computer science. We have developed high performance SAT solvers and MaxSAT solvers, achieving high rankings in some major international competitions. We have also developed local search based solvers specifically designed to search Ramsey graphs, whose performance exceeded the limit of more general purpose solvers.
We have also made a beginning of applying deep learning to discrete mathematics problems like search for Ramsey graphs.

Free Research Field

知能情報学

Academic Significance and Societal Importance of the Research Achievements

数学の数ある未解決問題の中でも、その解決に向けて計算科学的手段が本質的な役割を果たす場合が少なくない。その一例としてのRamsey数確定に関する問題において、SATソルバー等を利用した計算科学的アプローチが実際に奏功することが確認された。
本研究の主要な成果である高性能なSATソルバーやMaxSATソルバー、およびそれらを利用した問題解決手法は、数学に限らず様々な分野で活用され、多くの実践的な問題解決における貢献が期待される。