2007 Fiscal Year Final Research Report Summary
Construction of a Superrobust Computation Paradigm
| 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)
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| Project Period (FY) |
2003 – 2007
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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 |
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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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Research Products
(186 results)
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[Presentation] Defensive forecasting2005
Author(s)
V. Vovk, A. Takemura, G. Shafer
Organizer
Tenth International Workshop on ArtificialIntelligence and Statistic
Place of Presentation
Barbados
Year and Date
20050106-20050108
Description
「研究成果報告書概要(和文)」より
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[Presentation] Defensive forecasting2005
Author(s)
V. Vovk, A. Takemura, G. Shafer
Organizer
Tenth International Workshop on Artificial Intelligence and Statistic
Place of Presentation
Barbados
Year and Date
20050106-20050108
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Computing the similarity of two melodies2003
Author(s)
G. Aloupis, T. Fevens, S. Langerman, T. Matsui, A. Mesa, D. Rappaport, G. Toussaint
Organizer
15th Canadian Conference on Computational Geometry (CCCG2003)
Place of Presentation
Dalhousie University, Halifax
Year and Date
20030811-20030813
Description
「研究成果報告書概要(和文)」より
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[Book] へんな立体2007
Author(s)
杉原厚吉
Total Pages
143
Publisher
誠文堂新光社
Description
「研究成果報告書概要(和文)」より
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[Book] 形と動きの数理2006
Author(s)
杉原厚吉
Total Pages
210
Publisher
東京大学出版会
Description
「研究成果報告書概要(和文)」より
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[Book] 数学入門辞典2005
Author(s)
青本和彦, 上野健爾, 加藤和也, 神保道夫, 砂田利一, 高橋陽一郎, 深谷賢治, 俣野博, 室田一雄
Total Pages
728
Publisher
岩波書店
Description
「研究成果報告書概要(和文)」より
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