Mathematical Sciences: Computational Convexity

9530366 该奖项支持克利教授在组合学方面的研究。 在拟议的研究期间，重点将放在近年来被称为“计算凸性”的领域。 它形成了一个涉及凸几何、离散数学、计算机科学和运筹学等方面的接口。 本质上，它是研究高维凸体，特别是多面体的计算和算法方面。 这项研究是在组合数学的一般领域。 组合数学试图找到有效的方法来研究如何安排离散的对象集合。离散系统的行为对现代通信极为重要。 例如，大型网络的设计，如电话系统中的网络设计，以及计算机科学中的算法设计，都要处理离散的对象集，这就需要使用组合研究。此外，在这个项目中所寻求的枚举信息的类型已在机器人和运动规划问题的几何算法的设计中使用。

9530366 This award supports the research of Professor Klee in combinatorics. During the proposed research period, the emphasis will be in an area that has in recent years been called "Computational Convexity". It forms an interface that involves aspects of convex geometry, discrete mathematics, computer science, and operations research. In essence, it is the study of the computational and algorithmic aspects of high-dimensional convex bodies, especially polytopes. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research. In addition, the type of enumerative information being sought in this project has been of use in the design of geometric algorithms for problems in robotics and motion planning.