An O(log log m)-competitive Algorithm for Online Machine Minimization

TL;DR

This paper introduces an online scheduling algorithm that is exponentially more efficient in terms of machine usage, achieving O(log log m)-competitiveness for the machine minimization problem.

Contribution

It presents a novel online algorithm that improves the competitive ratio from O(log m) to O(log log m), advancing the theoretical understanding of online scheduling.

Findings

Achieves O(log log m)-competitiveness in online machine minimization.

Improves upon the previous O(log m) bound.

Provides a new approach for near-optimal online scheduling.

Abstract

This paper considers the online machine minimization problem, a basic real time scheduling problem. The setting for this problem consists of n jobs that arrive over time, where each job has a deadline by which it must be completed. The goal is to design an online scheduler that feasibly schedules the jobs on a nearly minimal number of machines. An algorithm is c-machine optimal if the algorithm will feasibly schedule a collection of jobs on cm machines if there exists a feasible schedule on m machines. For over two decades the best known result was a O(log P)-machine optimal algorithm, where P is the ratio of the maximum to minimum job size. In a recent breakthrough, a O(log m)-machine optimal algorithm was given. In this paper, we exponentially improve on this recent result by giving a O(log log m)-machine optimal algorithm.