The structure of designs

这项研究的目的是为了帮助人们理解离散结构的“互联性”属性。这将使人们更深入地理解复杂的离散结构，如网络，是如何相互作用的。这一领域的发展将提供对所涉及对象的结构的理解以及对其他组合问题的洞察。拟议的研究还将把研究结果应用于算法效率、软件测试和编码理论等不同的问题。这项研究还将为拟议研究领域内的HQP培训提供机会。具体的工作往往需要研究具有特定结构的设计的存在问题。将为此类设计和相关组合结构开发新的构造方法。这些方法通常分为两类。首先是一般的理论结构，用来寻找无限类的设计。其次，有一些计算机算法可以找到设计的个别实例。第一节课是关于结构问题的，而第二节课讨论的是算法问题。在短期内，特别感兴趣的领域将涉及我继续对可解决的结构进行调查。这也将扩大到对设计中更普遍的色度指数问题的调查。我还在进行一项关于设计分布内部和跨设计分布的结构存在的调查。最后，我开始研究阵列，这是一个特别感兴趣的领域，因为它在软件和网络测试中的应用。

The aim of this research is to facilitate an understanding of the 'interconnectedness' properties of discrete structures.  This will provide a deeper understanding of the way in which complex discrete structures, such as networks, interact with themselves. Development in this area will provide an understanding of the structure of the objects involved as well as insight into other combinatorial questions. The proposed research will also apply the results to such diverse questions as algorithmic efficacy, software testing and coding theory. The research will also provide an opportunity for the training of HQP within the areas of the proposed research. The specific work often entails research into existence questions of designs which have a particular structure. New constructive methods will be developed for such designs  and related combinatorial structures. These methods generally fall into two categories. Firstly there are general theoretical constructions, used to find infinite classes of designs. Secondly there are computer algorithms for finding individual instances of designs. The first class is of interest as regards structural questions, whereas the second class addresses algorithmic issues. In the short term the particular areas of interest will involve the continuation of my investigation into resolvable structures. This will also be broadened to an investigation of the more general problem of chromatic index in designs. I am also undertaking an investigation of the existence of structure within and across a distribution of designs. Finally I am starting to work in the area of covering arrays, an area of particular interest due to its applications to software and network testing.