Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model

TL;DR

This paper introduces a novel approximation scheme for online scheduling that achieves near-optimal competitive ratios on multiple machine models, marking the first such application in the online-list setting.

Contribution

It develops the first competitive-ratio approximation scheme for online scheduling on multiple machines, applicable to identical and related machine models.

Findings

Achieves arbitrarily close competitive ratios to the optimal.

Determines the optimal competitive ratio up to any desired accuracy.

First application of approximation schemes in the online-list model.

Abstract

We consider online scheduling on multiple machines for jobs arriving one-by-one with the objective of minimizing the makespan. For any number of identical parallel or uniformly related machines, we provide a competitive-ratio approximation scheme that computes an online algorithm whose competitive ratio is arbitrarily close to the best possible competitive ratio. We also determine this value up to any desired accuracy. This is the first application of competitive-ratio approximation schemes in the online-list model. The result proves the applicability of the concept in different online models. We expect that it fosters further research on other online problems.