The structure of designs

本研究的目的是促进对离散结构的“互联性”特性的理解。这将提供对复杂离散结构（如网络）相互作用方式的更深入理解。该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见解。建议的研究还将结果应用于算法功效，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卫生质量管理人员提供培训机会。具体的工作通常需要对具有特定结构的设计的存在问题进行研究。对于这种设计和相关的组合结构，将开发新的构造方法。这些方法一般分为两类。首先是一般的理论结构，用来寻找无限类的设计。其次，有计算机算法来查找设计的个别实例。第一类关注的是结构问题，而第二类关注的是算法问题。在短期内，特别感兴趣的领域将涉及我对可解决结构的继续调查。这也将扩大到对设计中色差指数的更普遍问题的调查。我也在进行一项关于结构存在的调查，这些结构存在于不同的设计中。最后，我开始研究涵盖数组的领域，由于它在软件和网络测试中的应用，这是一个特别有趣的领域。

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.