Grant: Discovery Grants Program - Individual

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.