Joint Research on Algorithms in Computational Geometry

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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.