T-Theory Applications to Online Algorithms for the Server Problem

Although largely unnoticed by the online algorithms community, T-theory, a field of discrete mathematics, has contributed to the development of several online algorithms for the k-server problem. A brief summary of the k-server problem, and some important application concepts of T-theory, are given. Additionally, a number of known k-server results are restated using the established terminology of T-theory. Lastly, a previously unpublished 3-competitiveness proof, using T-theory, for the Harmonic algorithm for two servers is presented. Keywords/Phrases: Double Coverage, Equipoise, Harmonic, Injective Hull, Isolation Index, Prime Metric, Random Slack, T-Theory, Tight Span, Trackless Online Algorithm School of Computer Science, University of Nevada, Las Vegas, NV 89154. Email: [email protected]. Research supported by NSF grant CCR-0312093. School of Computer Science, University of Nevada, Las Vegas, NV 89154. Email: [email protected]. Research supported by NSF grant CCR-0312093.