Mathematical Sciences: Computational Convexity

该奖项支持Klee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方面的接口。本质上，它是对高维凸体（本质上是多面体）的计算和算法方面的研究。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散集合。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，以及计算机科学中算法的设计都涉及离散对象，这就利用了组合研究。

This award supports the research of Professor Klee to work 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 (essentially polytopes). The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.