Gray Codes, Efficient Generation, and Structure in Combinatorial Families

这个奖项支持萨维奇教授在组合学方面的研究。组合算法领域的一个基本问题是有效地生成特定类中的项，使每个项只生成一次。要逐步提高组合生成的效率，不仅需要良好的数据结构和算法设计技术，更需要对所涉及的组合类的结构有一些新的认识。这些结构问题属于离散数学、图论、群论和组合学中众所周知的开放问题。萨维奇教授要解决的就是这类问题。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 Savage to work in combinatorics. One of the fundamental problems in the area of combinatorial algorithms is that of efficiently generating items in a particular class in such a way that each item is generated exactly once. Asymptotic improvement in the efficiency of combinatorial generation requires not only good data structures and algorithm design techniques, but more often, some new insight into the structure of the combinatorial class involved. These structure questions are in the realm of well-known open problems in discrete mathematics, graph theory, group theory, and combinatorics. It is these type of problems that Professor Savage will address. 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.