2019 Fiscal Year Final Research Report
Study on Theory of Combinatorial Optimization with Applications to Robust Network Design
| Project/Area Number |
16K16010
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | Kyoto University (2018-2019)
University of Tsukuba (2016-2017) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 組合せ最適化 / アルゴリズム / グラフ |
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| Outline of Final Research Achievements |
In this study, we developed a theory of combinatorial optimization problems arising in the context of robust network design. We dealt with generalized problems that are not dependent on a specific network or a specific situation. We designed efficient algorithms for many combinatorial optimization problems and analyzed their performance. In particular, we gave a first polynomial-time algorithm for the weighted linear matroid parity problem, which had been open for more than 30 years.
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| Free Research Field |
組合せ最適化
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，様々な組合せ最適化問題に対して効率的アルゴリズムを与えた．扱った問題はいずれも一般性の高い問題であるため，現実のネットワーク設計への応用に役立つと考えられる．また，本研究で解決した重み付き線形マトロイドパリティ問題は，30年以上未解決だった問題であり，この問題に対して初の多項式時間アルゴリズムを与えたことは，理論研究において大きな意義のある成果である．
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