$k$-Servers with a Smile: Online Algorithms via Projections

TL;DR

This paper introduces a new online algorithm for the $k$-server problem on trees and HSTs using Bregman projections, achieving competitive ratios comparable to recent mirror-descent-based methods.

Contribution

It presents a novel projection-based algorithm for the $k$-server problem that matches recent state-of-the-art competitive ratios on trees and HSTs.

Findings

Achieves competitive ratios similar to recent mirror-descent algorithms.

Uses Bregman projections to develop the online algorithm.

Applicable to trees and HSTs for the $k$-server problem.

Abstract

We consider the $k$-server problem on trees and HSTs. We give an algorithm based on Bregman projections. This algorithm has a competitive ratios that match some of the recent results given by Bubeck et al. (STOC 2018), whose algorithm was based on mirror-descent-based continuous dynamics prescribed via a differential inclusion.