Computational Geometry and Discrete Optimization in Architecture and Urban Planning

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(1) Molecular framework that models a molecular structure is an important model which is used to predict protein motion. There was a famous open problem called “Molecular conjecture” that deals with the rigidity of molecular frameworks in terms of combinatorial rigidity which was posed more than 25 five years ago. In this project, we could succeed in affirmatively solving this problem.(2) As for the research of dynamic flow network that models the problem of finding an optimal evacuation planning, we developed a polynomial time algorithm that finds a universally quickest flow. Also, we applied our algorithm to evaluate the appropriateness of capacities of evacuation centers in Kyoto City as well as tsunami evacuation buildings in Okisu area of Tokushima Cit y.