Mathematical Sciences: The Probabilistic Method

这个奖支持斯宾塞教授在组合学方面的研究。具体地说，斯宾塞教授正在开发用于处理组合学问题的概率方法。离散数学和计算机科学之间的相互作用提出了一种算法观点。许多概率存在性证明为相应的算法问题提供了立即有效的随机化过程，在某些情况下，这些过程可以被非随机化并转换为确定性过程。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 Spencer to work in combinatorics. Specifically, Professor Spencer is developing the Probabilistic Method for use in dealing with problems in combinatorics. The interplay between discrete mathematics and computer science suggests an algorithmic viewpoint. Many probabilistic proofs of existence supply immediately efficient randomized procedures for the corresponding algorithmic problems, and in some cases these procedures can be derandomized and converted into deterministic ones. 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.