The structure of designs

这项研究的目的是促进离散结构的“互连性”的属性的理解。 这将提供对复杂离散结构（如网络）与自身相互作用的方式的更深入理解。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。拟议中的研究还将把结果应用于算法功效、软件测试和编码理论等各种问题。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。新的建设性的方法将开发这样的设计和相关的组合结构。这些方法一般分为两类。首先有一般的理论结构，用于找到无限类的设计。其次，有计算机算法来找到设计的个别实例。第一类是关于结构问题的兴趣，而第二类解决算法问题。在短期内，我感兴趣的特定领域将包括对可分解结构的继续研究。这也将扩大到更普遍的问题的调查色指数的设计。我也在调查设计分布中的结构存在。最后，我开始在覆盖阵列领域工作，这是一个特别感兴趣的领域，因为它应用于软件和网络测试。

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.