| Project/Area Number |
15100001
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
Software
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| Research Institution | The University of Tokyo |
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Principal Investigator |
SUGIHARA Kokichi The University of Tokyo, Graduate School of Information Science and Technology, Professor (40144117)
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| Co-Investigator(Kenkyū-buntansha) |
OYANAGI Yoshio Kogakuin University, Faculty of Informatics, Professor (60011673)
YAMAMOTO Hirosuke The University of Tokyo, Graduate School of Frontier Sciences and Technology, Professor (30136212)
MUROTA Kazuo The University of Tokyo, Graduate School of Information Science and Technology, Professor (50134466)
IMAI Hiroshi The University of Tokyo, Graduate School of Frontier Sciences and Technology, Professor (80183010)
SUGIHARA Masaaki The University of Tokyo, Graduate School of Frontier Sciences and Technology, Professor (80154483)
村重 淳 東京大学, 大学院新領域創成科学研究科, 助教授 (40302749)
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| Project Period (FY) |
2003 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥117,650,000 (Direct Cost: ¥90,500,000、Indirect Cost: ¥27,150,000)
Fiscal Year 2007: ¥22,880,000 (Direct Cost: ¥17,600,000、Indirect Cost: ¥5,280,000)
Fiscal Year 2006: ¥23,920,000 (Direct Cost: ¥18,400,000、Indirect Cost: ¥5,520,000)
Fiscal Year 2005: ¥22,100,000 (Direct Cost: ¥17,000,000、Indirect Cost: ¥5,100,000)
Fiscal Year 2004: ¥26,260,000 (Direct Cost: ¥20,200,000、Indirect Cost: ¥6,060,000)
Fiscal Year 2003: ¥22,490,000 (Direct Cost: ¥17,300,000、Indirect Cost: ¥5,190,000)
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| Keywords | robust algorithms / structural invariances / extension of object worlds / uncertainty modeling / assumption-free world / robust computation principles / physical simulation / robust control / 非線形波動方程式 / 独立粒子法 / クロネッカー標準形 / ゲーム論的確率論 / ロバスト混合整数計画法 / 記号摂動 / ロバスト性 / メッシュ簡略化 / 保存則再現有限要素法 / 再帰系列 / 離散構造 / ボート航行距離方程式 / カッターバス / 超図形 / ディジタルトポロジー / パーフェクトサンプリング / 粒子追跡法 / ロバスト計算 / 精度保証区間 / 幾何計算 / 近似アルゴリズム / 離散凸関数 / 並列計算 |
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| Research Abstract |
The goal of this research was to construct a paradigm for designing robust algorithms in a wide area of computation. To achieve this goal, we developed robust computation techniques in individual areas of computations such as physical simulation, parallel and distributed computation, computation for control, geometric computation, discrete optimization, information coding, and quantum computation, and from them we tried to extract common and transversal principles applicable to designing robust algorithms in a wide area of computation. As the results, we succeeded in extracting the following general principles. The first principle is to use structural invariances that lay behind the computation. Applying this principle, we developed robust geometric algorithms based on topologically consistent graph manipulations, robust methods for solving partial differential equations based on physical laws behind, robust control based on causal relations among events, and robust algebraic computations based on sign patterns and zero-nonzero patterns. The second principle is to remove restrictions by extending the object world; examples are hyperfigure algebra and symbolic perturbation in geometric computations. The third principle is to remove uncertainty by restricting the object world. The other principles include modeling of uncertainty for coping with the worst case, and the generalizations by the removal of unrealistic assumptions of the computational world. These principles have also been applied to individual computation such as discrete optimization, mathematical programming, coding, matrix computation, integer programming related to practical problems. Thus we established a first version of superrobust computation paradigm.
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