Dynamic beats fixed: On phase-based algorithms for file migration

TL;DR

This paper introduces a new deterministic phase-based online file migration algorithm that dynamically adapts phase lengths, achieving a better competitive ratio than the longstanding previous best.

Contribution

It presents a novel dynamic phase-length algorithm that improves the competitive ratio for online file migration over the classic fixed-phase approach.

Findings

Achieved a 4-competitive ratio, beating the 4.086 ratio of the previous best.

Demonstrated the limitations of fixed-length phase algorithms with an adversarial graph modification.

Used linear model analysis to optimize phase adaptation for better performance.

Abstract

We construct a deterministic 4-competitive algorithm for the online file migration problem, beating the currently best 20-year-old, 4.086-competitive MTLM algorithm by Bartal et al. (SODA 1997). Like MTLM, our algorithm also operates in phases, but it adapts their lengths dynamically depending on the geometry of requests seen so far. The improvement was obtained by carefully analyzing a linear model (factor-revealing LP) of a single phase of the algorithm. We also show that if an online algorithm operates in phases of fixed length and the adversary is able to modify the graph between phases, then the competitive ratio is at least 4.086.