Randomized algorithm for the k-server problem on decomposable spaces

TL;DR

This paper introduces a method to extend randomized algorithms for the k-server problem to decomposable metric spaces, achieving competitive ratios of at most O(log k) and providing o(k)-competitive solutions for specific spaces like HSTs.

Contribution

The paper presents a novel extension technique for existing algorithms to larger decomposable metric spaces, improving competitive ratios for the randomized k-server problem.

Findings

Achieves O(log k) competitive ratio in extended spaces

Provides o(k)-competitive algorithms for certain metric spaces

Utilizes HSTs for probabilistic metric space approximation

Abstract

We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log k). This method yields o(k)-competitive algorithms solving the randomized k-server problem, for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree). HSTs are important tools for probabilistic approximation of metric spaces.