Computational Geometry and Discrete Optimization in Architecture and Urban Planning

(1)模拟分子结构的分子框架是预测蛋白质运动的重要模型。有一个著名的开放问题叫做“分子猜想”它从组合刚性的角度来研究分子框架的刚性这是在25年前提出的。在这个项目中，我们可以成功地解决这个问题。(2)对于寻找最优疏散规划问题的动态流网络的研究，我们开发了一个多项式时间算法来寻找一个普遍最快的流。此外，我们还应用我们的算法评估了京都市疏散中心以及德岛市Okisu地区海啸疏散建筑的能力的适宜性。

(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.