| Project/Area Number |
16K12393
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Theory of informatics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Research Collaborator |
Nakamura Kengo
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ネットワーク問題 / グラフ分解 / 最大フロー / 深さ優先探索 / グラフ |
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| Outline of Final Research Achievements |
We have developed algorithms for various network problems based on graph decomposition. We evaluated time complexities for s-t max flow, all pairs max flow, mininum cut, single source shortest paths, and all pairs shortest paths, using the size of the largest triconnected components in the graph as a parameter. These algorithms are faster than existing ones if the size of the largest triconnected components is small. This means we can say that the size of the largest triconnected components is a parameter on difficulties of network problems.
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| Academic Significance and Societal Importance of the Research Achievements |
グラフに関する問題を解くアルゴリズムとしては，木分解に基づくアルゴリズムが多く存在するが，それらは木幅が小さい場合しか適用できない．本研究で開発するアルゴリズムは異なる分解に基づくため，木幅が大きいグラフに対しても適用できる．また，木分解と異なり，問題によっては計算量がパラメタの指数では無く多項式に比例するようになることがある．これにより，多くのグラフに対して実用的なアルゴリズムを開発できるようになることが期待される．
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