| Project/Area Number |
20500012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
NAGAMOCHI Hiroshi Kyoto University, 大学院・情報学研究科, 教授 (70202231)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUNAGA Takuro 京都大学, 大学院・情報学研究科, 助教 (60452314)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 可視化 / 詰め込み問題 / パッキング / アルゴリズム / 最適化 / 機械学習 / グラフ描 / 準ニュートン法 / 離散最適化 / 配置問題 / グラフ描画 / ルーティング問題 / 近似解法 / 計算幾何学 / 組合せ最適 / 図形配置 / データ構造 / 非線形最適化 / 情報可視化 |
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| Research Abstract |
In this study, we proposed "Multi-sphere Scheme" to efficiently pack given two- or three-dimensional objects in a compact space, designed all the components of the scheme, and investigated fundamental theory on geometrical packings and graph drawings. We designed an algorithm that can directly transform given triangle-mesh data into data for Multi-sphere Scheme based on a graph-theoretical analysis. We developed a 3D visual interface for Multi-sphere Scheme, by which we can easily check computational results in a visualized form. We greatly improved our solver for packing rectangles so that a long-standing open benchmark instance is solved for the first time by our new solver. As for the theory part, we found a 2D representation of triconnected graphs so that a useful triconnected decomposition can be easily obtained, and a characterization of the graphs of non-convex polytopes in a certain class.In particular, the latter result is the first such result since Steinitz' theorem, a characterization of the graphs of convex polytopes is found 80 years ago.
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