Deterministic 3-Server on a Circle and the Limitation of Canonical Potentials
Abstract
The deterministic -server conjecture states that there is a -competitive deterministic algorithm for the -server problem for any metric space. We show that the work function algorithm is -competitive for the -server problem on circle metrics, a case left open by Coester and Koutsoupias (2021). Our analysis follows the existing framework but introduces a new potential function which may be viewed as a relaxation of the counterpart by Coester and Koutsoupias (2021). We further notice that the new potential function and many existing ones can be rewritten in a canonical form. Through a computer-aided verification, however, we find that no such canonical potential function can resolve the deterministic -server conjecture for general metric spaces under the current analysis framework.
Cite
@article{arxiv.2205.08103,
title = {Deterministic 3-Server on a Circle and the Limitation of Canonical Potentials},
author = {Zhiyi Huang and Hanwen Zhang},
journal= {arXiv preprint arXiv:2205.08103},
year = {2022}
}