RUI: Computer Search for Elusive Combinatorial Congfigurations: A Research Toolchest

在过去的几年里，计算机在寻找新的特殊组合构型以及证明它们不存在方面的作用越来越大。它现在是这一领域研究中不可缺少的工具。在世界范围内，已经有许多尝试在这个方向上构建合适的软件，但是没有一个具有这里提出的特定目标范围。四个感兴趣的领域是：平衡设计，拉姆齐图，垂直阵列和集合覆盖系统。以前在这些领域的研究反复要求类似的算法，这些算法以一种特殊的方式实现，取决于特定的情况。在同一地区甚至有相同算法的变体。这个为期一年的项目的主要目标是使用商定的统一数据结构来改进、简化和打包现有的算法。有了这些算法，人们可以把更多的注意力放在集合系统的理论性质上，而不是放在规划上。还将特别注意寻找一些新的重要配置。

The role of the computer in the search for new exceptional combinatorial configurations, as well as in the proofs of their nonexistence, has been increasing over the last few years. It is now an indispensable tool in research in this area. There have been many attempts to build appropriate software in this direction worldwide, but none with the range of specific goals proposed here. The four areas of interest are: balance designs, Ramsey graphs, perpendicular arrays and set coverings systems. Previous research in these areas repeatedly called for similar algorithms, which were implemented in an ad hoc manner, depending on the particular situation. There were even variations of the same algorithm within the same area. A principal goal of this one year project is to refine, streamline and package the existing algorithms, using agreed upon uniform data structures. With these algorithms one can devote more attention on the theoretical properties of the set systems rather than on programming. Particular attention will also be focused on finding some new important configuations.