Random graph processes and optimisation

Printed on archival quality paper. Random graph processes are most often used to investigate theoretical questions about random graphs. A randomised algorithm can be defined specifically for the purpose of finding some structure in a graph, such as a matching, a colouring or a particular kind of subgraph. Properties of the related random graph process then suggest properties, or bounds on properties, of the structure. In this thesis, we use a random graph process to analyse a particular load balancing algorithm from theoretical computer science. By doing so, we demonstrate that random graph processes may also be used to analyse other algorithms and systems of a random nature, from areas such as computer science, telecom-munications and other areas of engineering and mathematics. Moreover, this approach can lead to theoretical results on the performance of algorithms that are difficult to obtain by other methods. In the course of our analysis we are also led to some results of the first kind, relating to the structure of the random graph. The particular algorithm that we analyse is a randomised algorithm for an off-line loa