A Computational Approach to Study Ramsey Numbers
| Project/Area Number |
17K00307
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Intelligent informatics
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| Research Institution | Kyushu University |
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Principal Investigator |
Fujita Hiroshi 九州大学, システム情報科学研究院, 准教授 (70284552)
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| 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)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | Ramsey number / SAT solver / Ramseyグラフ / 局所探索 / 深層学習 / Python / Ramsey数 / SATソルバー / MaxSATソルバー / 基数制約 |
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| 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.
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| 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。
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Report
(4 results)
Research Products
(7 results)
