On the Monotonicity of Work Function in k-Server Conjecture

TL;DR

This paper challenges a key assumption in the k-server conjecture by demonstrating that the work function's monotonicity does not always hold, impacting the understanding of the algorithm's theoretical foundations.

Contribution

It identifies a flaw in the presumed monotonicity property of the work function, which is fundamental to the k-server conjecture.

Findings

Monotonicity of the work function is not always valid.

The flaw affects the theoretical guarantees of the work function algorithm.

Implications for future research on k-server algorithms.

Abstract

This paper presents a mistake in work function algorithm of k-server conjecture. That is, the monotonicity of the work function is not always true.