Joint Research on Algorithms in Computational Geometry

计算几何算法联合研究

基本信息

批准号：
06044058
负责人：
IMAI Hiroshi
金额：
$ 4.1万
依托单位：
University of TOKYO
依托单位国家：
日本
项目类别：
Grant-in-Aid for international Scientific Research
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

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.

日本文部科学省联合研究国际科学研究计划的科学研究资助已于1994年和1995学年进行。该项目的应用是，将日本、加拿大和美国的计算几何领域活跃的研究人员聚集在一起，根据该小组每个成员的建立来制定该领域的新课题。事实上，一些小组成员曾有机会在加拿大和日本进行过短期合作，但由于时间和人数的限制，这种联合研究的规模很小。通过这个项目，我们组的所有研究人员可以聚集在一起讨论当今最活跃的话题。通过这个项目，我们在我们成员提出的技术的基础上发展了几何枚举、生成和计数的理论。具体来说，反向搜索、二元决策图和多面方法被证明是解决现有方法无法解决的大尺寸几何问题的强大工具。这是基于本次援助金在加拿大和日本多次交换想法而实现的。事实上，我们课题组的国际合作已经扩展到亚太地区，吸引了很多这些领域的研究人员加入我们。从论文列表可以看出，我们的成果已经发表。一本著名的日语出版物是 David Avis 和 Hiroshi Imai 所著的《计算几何》一书。关于三角测量的编程包，今年将在第十二届 ACM 计算几何研讨会上进行技术演示和视频演示，这是该领域最大的活动之一。