Settling the Randomized k-sever Conjecture on Some Special Metrics

TL;DR

This paper proves that for specific metric spaces like line, circle, and HST, there are efficient randomized algorithms for the k-sever problem, and provides bounds for general metrics, advancing understanding of this problem.

Contribution

It settles the randomized k-sever conjecture for certain metric spaces and establishes competitive bounds for general metrics.

Findings

O(log k)-competitive algorithms for line, circle, HST

O(log k log n)-competitive algorithm for general metrics

Advances theoretical understanding of the k-sever problem

Abstract

In this paper, we settle the randomized $k$-sever conjecture for the following metric spaces: line, circle, Hierarchically well-separated tree (HST). Specially, we show that there are $O(\log k)$-competitive randomized $k$-sever algorithms for above metric spaces. For any general metric space with $n$ points, we show that there is an $O( \log k \log n)$-competitive randomized $k$-sever algorithm.