Mathematical Sciences: Computational Convexity

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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.