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 sub graph. 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, telecommunications 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 load balancing problem with two choices. The load balancing algorithm, in an initial stage, mirrors an algorithm which finds the k-core of a graph. This latter algorithm and the related random graph process have been previously analysed by Pittel, Spencer and Wormald, using a differential equation method, to determine the thresholds for the existence of a k-core in a random graph. We modify their approach by using a random pseudograph model due to Bollobas and Frieze, and Chvatal, in place of the uniform random graph. This makes the analysis somewhat simpler, and leads to a shortened derivation of the thresholds and other properties of k-cores.(For complete abstract open document)
| Identifer | oai:union.ndltd.org:ADTP/245541 |
| Creators | Cain, Julie A |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Terms and Conditions: Copyright in works deposited in the University of Melbourne Eprints Repository (UMER) is retained by the copyright owner. The work may not be altered without permission from the copyright owner. Readers may only, download, print, and save electronic copies of whole works for their own personal non-commercial use. Any use that exceeds these limits requires permission from the copyright owner. Attribution is essential when quoting or paraphrasing from these works., Open Access |
Page generated in 0.0016 seconds