T-Theory Applications to Online Algorithms for the Server Problem

TL;DR

This paper explores the application of T-theory, a discrete mathematics field, to online algorithms for the k-server problem, highlighting new insights and a novel competitiveness proof for the Harmonic algorithm.

Contribution

It introduces T-theory to the online algorithms community, restates known results in T-theory terms, and provides a new competitiveness proof for the Harmonic algorithm.

Findings

T-theory offers valuable tools for analyzing online algorithms.

A new 3-competitiveness proof for the Harmonic algorithm is presented.

T-theory-based analysis simplifies understanding of k-server algorithms.

Abstract

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 Lastly, a previously unpublished 3-competitiveness proof, using T-theory, for the Harmonic algorithm for two servers is presented.