一个O(Log Log m)竞争的在线机器最小化算法

Sungjin Im, Benjamin Moseley, K. Pruhs, C. Stein
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引用次数: 5

摘要

本文研究在线机器最小化问题,这是一个基本的实时调度问题。此问题的设置由n个随时间到达的作业组成,其中每个作业都有必须完成的截止日期。目标是设计一个在线调度器,它可以在几乎最少数量的机器上调度作业。如果在m台机器上存在可行的调度,那么该算法将在c·m台机器上可行地调度一组作业,则该算法是c机最优的。二十多年来,最著名的结果是O(log P)机器最优算法,其中P是最大与最小作业大小的比率。在最近的一个突破中,给出了一个O(log m)机最优算法。在本文中,我们通过给出一个O(log log m)机最优算法,指数地改进了这个最近的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An O(Log Log m)-Competitive Algorithm for Online Machine Minimization
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 c ·m 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.
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