Optimization Problems in Computational Geometry

这个项目的总主题是几何问题优化算法的设计、分析和实现。研究将集中在以下几个方面： 几何网络：如何构建连接一组给定站点的良好网络。给定这样一个网络，如何利用几何信息来计算(精确或近似)任意两个给定站点之间的最短路径。考虑到这样一个网络，如何对其进行修改，使所有站点都有良好的连接。 几何数据结构：如何组织几何数据，以便可以计算包含在查询区域中的数据子集的信息性“摘要”。 计算机辅助设计中的几何问题：如何将计算几何技术应用于加速计算机辅助制造中的算法过程。

The general theme in this project is the design, analysis, and implementation of optimization algorithms for geometric problems. The research will concentrate on the following topics: Geometric networks: How to construct a good network that connects a given set of sites. Given such a network, how to use geometric information to compute (exact or approximate) shortest paths between any two given sites. Given such a network, how to modify it so that all sites have good connections. Geometric data structures: How to organize geometric data, such that an informative "summary" of the subset of the data that is contained in a query region can be computed. Geometric problems in computer-aided design: How to apply techniques from computational geometry to speed-up algorithmic processes in computer-aided manufacturing.