Towards Simpler Algorithms in Computational Geometry

计算几何关注涉及大量几何数据的问题的算法设计和分析。该项目寻求更简单、更有效的算法来解决计算几何中的基本问题，这些问题在计算机图形学、计算机视觉、数据库和统计学中都有应用。要研究的问题包括几何优化、基本几何结构的构造以及处理几何查询的数据结构的设计。这些问题将使用随机化、近似和修正悲观最坏情况分析的技术来解决。

Computational geometry concerns the design and analysis of algorithms for problems involving large amounts of geometric data. This project seeks simpler and more efficient algorithms for fundamental problems in computational geometry that have applications in computer graphics, computer vision, databases, and statistics. The problems to be studied include geometric optimization, construction of basic geometric structures, and the design of data structures for processing geometric queries. The problems will be approached using randomization, approximation, and techniques for correcting pessimistic worst-case analyses.