On the Additive Constant of the k-server Work Function Algorithm

TL;DR

This paper proves that if the Work Function Algorithm for the k-server problem is c-competitive, then it is strictly 2c-competitive, leading to a new bound of (4k-2)-competitiveness.

Contribution

It establishes a new relationship between c-competitiveness and strict competitiveness for the Work Function Algorithm, improving known bounds.

Findings

If WFA is c-competitive, then it is strictly 2c-competitive.

WFA is strictly (4k-2)-competitive based on prior results.

Provides a tighter bound on the competitiveness of WFA.

Abstract

We consider the Work Function Algorithm for the k-server problem. We show that if the Work Function Algorithm is c-competitive, then it is also strictly (2c)-competitive. As a consequence of [Koutsoupias and Papadimitriou, JACM 1995] this also shows that the Work Function Algorithm is strictly (4k-2)-competitive.