Memoryless Algorithms for the Generalized $k$-server Problem on Uniform Metrics

TL;DR

This paper analyzes memoryless algorithms for the generalized k-server problem on uniform metrics, establishing tight bounds on their competitive ratio and demonstrating the optimality of the Harmonic Algorithm.

Contribution

It provides tight bounds of Θ(k!) on the competitive ratio of memoryless algorithms and shows that the Harmonic Algorithm achieves this bound, improving previous exponential bounds.

Findings

Harmonic Algorithm achieves the tight Θ(k!) competitive ratio.

Established matching lower bounds for memoryless algorithms.

Improved upon previous doubly-exponential bounds for uniform metrics with weights.

Abstract

We consider the generalized $k$-server problem on uniform metrics. We study the power of memoryless algorithms and show tight bounds of $\Theta(k!)$ on their competitive ratio. In particular we show that the \textit{Harmonic Algorithm} achieves this competitive ratio and provide matching lower bounds. This improves the $\approx 2^{2^k}$ doubly-exponential bound of Chiplunkar and Vishwanathan for the more general setting of uniform metrics with different weights.