| Project/Area Number |
17K00013
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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 |
Theory of informatics
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| Research Institution | Toyohashi University of Technology |
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Principal Investigator |
Fujito Toshihiro 豊橋技術科学大学, 工学(系)研究科(研究院), 教授 (00271073)
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| Co-Investigator(Kenkyū-buntansha) |
藤原 洋志 信州大学, 学術研究院工学系, 准教授 (80434893)
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 組合せ最適化問題 / NP困難問題 / 近似アルゴリズム / 辺支配集合 / bマッチング / 次数制限除去問題 / power被覆 / 恒久的被覆問題 / 連結頂点被覆 / 弦グラフ / 辺支配集合問題 / 有向グラフ / 頂点被覆問題 / Power頂点被覆 / Power Vertex Cover / 立体ピクロス / 最小ヒント数問題 / 頂点除去問題 / 制限次数除去問題 / パス頂点被覆 / アルゴリズム / 理論保証 |
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| Outline of Final Research Achievements |
1. Some NP-hard optimization problems on graphs and networks have been considered such as bounded degree deletion, connected path vertex cover, and 4-edge dominating set. A new algorithm is designed and an improved approximation guarantee is obtained for each of those problems considered.
2. It is required in the eternal connected vertex cover problem to compute the minimum number of guards to be placed on vertices of a given graph G such that they can repel any sequence of attacks on edges in G while keeping a connected formation. It is shown that 1) the problem is polynomial on chordal graphs, 2) it is NP-hard on locally connected graphs, and 3) it is approximable within 2 on general graphs.
3. A new problem called "power bounded degree deletion" is introduced by extending the cover condition in bounded degree deletion. It is shown how to approximate this new problem within 2+log b, matching the best approximation known for the original problem.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究で対象とした組合せ最適化問題はいずれも実用上重要なものでありながら，NP困難，つまり高速計算が難しい問題です．特に近年のデータの大規模化に伴い，大量のデータを処理できる高速アルゴリズムの開発は必須であり，その中で解品質・解精度を改良することは，学術的にも重要と考えられます．
また，power版へ問題を拡張することは，より現実に即した問題設定において解決法を追求することであり，実用問題への応用等を考える上で不可欠です．
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