| Project/Area Number |
06044058
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | Joint Research |
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| Research Institution | University of TOKYO |
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Principal Investigator |
IMAI Hiroshi Graduate School of Science, University of Tokyo, Associate Professor, 大学院・理学系研究科, 助教授 (80183010)
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| Co-Investigator(Kenkyū-buntansha) |
ASAI Kenichi Graduate School of Science, University of Tokyo, Research Associate, 大学院・理学系研究科, 助手 (10262156)
IWATA Satoru Research Institute of Mathematical Sciences, Kyoto University, Research Associat, 数理解析研究所, 助手 (00263161)
TSUCHIYA Takashi The Institute of Statistical Mathematics, Research Associate, 助手 (00188575)
INAGAKI Hiroshi Toyoda College of Technology, Lecturer, 助手 (40213110)
IMAI Keiko Faculty of Science and Engineering, Chuo University, Associate Professor, 理工学部, 助教授 (70203289)
ASANO Takao Faculty of Science and Engineering, Chuo University, Professor, 理工学部, 教授 (90124544)
SUGIHARA Kokichi Graduate School of Engineering, University of Tokyo, Professor, 大学院・工学系研究科, 教授 (40144117)
EDELSBRUNNER Helbert Faculty of Engineering, Illinois University, Professor, 工学部, 教授
RAPPAPORT David Department of Computer and Information Science, Queen's University, Assocrate Pr, 工学部, 副教授
TOUSSAINT Godfried School of Computer Science, McGill University, Professor, 理学部, 教授
AVIS David School of Computer Science, McGill University, Professor, 理学部, 教授
HELBERT Edel Illinois大学, 工学部, 教授
DAVID Rappap Queens大学, 工学部, 副教授
GODFRIED Tou McGill大学, 理学部, 教授
DAVID Avis McGill大学, 理学部, 教授
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| Project Period (FY) |
1994 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥6,400,000 (Direct Cost: ¥6,400,000)
Fiscal Year 1995: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1994: ¥3,300,000 (Direct Cost: ¥3,300,000)
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| Keywords | Computational geometry / combinatorial optimization / combinatorics / reverse search / discrete geometry / mathematical programming / computational complexity / binary decision diagrams / アルゴリズム / Voronoi図 / アレジメント / 凸多面体 / 三角形分割 / クラスタリング |
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| Research Abstract |
This Grant-in Aid for Scientific Research in the International Scientific Research Program for Joint Research of the Ministry of Education, Science, Sports and Culture of Japan have been carried out for 1994 and 1995 academic years. This project was applied to the program by bringing making active researchers in computational geometry in Japan, Canada and US together to work out for new topics in the field based on the establishments of each member of this group. In fact, some of the group members had chances to work together in Canada and Japan for a short period, but such joint research was a very small-scale one due to the constraints about the time and the number of members. By this project, all the researchers in our group can gather together to discuss the most active topics nowadays.
By this project, we have developed the theory of geometric enumeration, generation and counting based on the techniques proposed by our members. Specifically, reverse search, binary decision diagrams and polytopal approaches are demonstrated to be powerful tools to solve geometric problems of large size which could not be solved by the existing methods. This was achieved by exchanging ideas in Canada and Japan several times based on this Grant-in-Aid. In fact, the international cooperation between our group has been extended to Asian/Pacific Area by attracting many research in these areas to join us.
Our results have been published as is seen from the list of papers. A notable publication in Japanese is a book by David Avis and Hiroshi Imai on Computational Geometry. About the programming package on triangulations, a technical presentation and a video presentation will be done at the 12th ACM Symposium on Computational Geometry this year, which is one of the biggest event in the field.
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