A Polylogarithmic-Competitive Algorithm for the k-Server Problem

TL;DR

This paper introduces the first randomized online algorithm for the k-server problem with a polylogarithmic competitive ratio, significantly improving previous deterministic bounds on arbitrary finite metric spaces.

Contribution

It presents a novel randomized algorithm achieving a polylogarithmic competitive ratio for the k-server problem on any finite metric space.

Findings

Achieves a competitive ratio of O(log^3 n log^2 k log log n)

Improves upon deterministic algorithms when n is sub-exponential in k

First to provide a polylogarithmic-competitive randomized solution

Abstract

We give the first polylogarithmic-competitive randomized online algorithm for the $k$-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of O(log^3 n log^2 k log log n) for any metric space on n points. Our algorithm improves upon the deterministic (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou [J.ACM'95] whenever n is sub-exponential in k.