An improved greedy algorithm for stochastic online scheduling on unrelated machines

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Sven Jäger
{"title":"An improved greedy algorithm for stochastic online scheduling on unrelated machines","authors":"Sven Jäger","doi":"10.1016/j.disopt.2022.100753","DOIUrl":null,"url":null,"abstract":"<div><p>Most practical scheduling applications involve some uncertainty about the arriving times and lengths of the jobs. Stochastic online scheduling is a well-established model capturing this. Here the arrivals occur online, while the processing times are random. For this model, Gupta, Moseley, Uetz, and Xie recently devised an efficient policy for non-preemptive scheduling on unrelated machines with the objective to minimize the expected total weighted completion time. We improve upon this policy by adroitly combining greedy job assignment with <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>-point scheduling on each machine. In this way we obtain a <span><math><mrow><mrow><mo>(</mo><mn>3</mn><mo>+</mo><msqrt><mrow><mn>5</mn></mrow></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>Δ</mi><mo>)</mo></mrow></mrow></math></span>-competitive deterministic and an <span><math><mrow><mo>(</mo><mn>8</mn><mo>+</mo><mn>4</mn><mi>Δ</mi><mo>)</mo></mrow></math></span>-competitive randomized stochastic online scheduling policy, where <span><math><mi>Δ</mi></math></span> is an upper bound on the squared coefficients of variation of the processing times. We also give constant performance guarantees for these policies within the class of all fixed-assignment policies. The <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>-point scheduling on a single machine can be enhanced when the upper bound <span><math><mi>Δ</mi></math></span> is known a priori or the processing times are known to be <span><math><mi>δ</mi></math></span>-NBUE for some <span><math><mrow><mi>δ</mi><mo>≥</mo><mn>1</mn></mrow></math></span><span>. This implies improved competitive ratios for unrelated machines but may also be of independent interest.</span></p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528622000585","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1

Abstract

Most practical scheduling applications involve some uncertainty about the arriving times and lengths of the jobs. Stochastic online scheduling is a well-established model capturing this. Here the arrivals occur online, while the processing times are random. For this model, Gupta, Moseley, Uetz, and Xie recently devised an efficient policy for non-preemptive scheduling on unrelated machines with the objective to minimize the expected total weighted completion time. We improve upon this policy by adroitly combining greedy job assignment with αj-point scheduling on each machine. In this way we obtain a (3+5)(2+Δ)-competitive deterministic and an (8+4Δ)-competitive randomized stochastic online scheduling policy, where Δ is an upper bound on the squared coefficients of variation of the processing times. We also give constant performance guarantees for these policies within the class of all fixed-assignment policies. The αj-point scheduling on a single machine can be enhanced when the upper bound Δ is known a priori or the processing times are known to be δ-NBUE for some δ1. This implies improved competitive ratios for unrelated machines but may also be of independent interest.

非相关机器随机在线调度的改进贪心算法
大多数实际的调度应用程序都涉及到作业到达时间和长度的一些不确定性。随机在线调度是一个公认的模型,捕捉到了这一点。在这里,到达是在线的,而处理时间是随机的。对于该模型,Gupta、Moseley、Uetz和Xie最近设计了一种在不相关机器上进行非抢占式调度的有效策略,目的是最小化预期的总加权完成时间。我们通过巧妙地将贪婪作业分配与每台机器上的αj点调度相结合,改进了这一策略。通过这种方式,我们获得了一个(3+5)(2+Δ)竞争确定性和(8+4Δ)竞争随机在线调度策略,其中Δ是处理时间的平方变化系数的上界。我们还在所有固定分配策略的类别中为这些策略提供恒定的性能保证。当上界Δ先验已知或处理时间已知为δ-NBUE时,对于某些δ≥1,可以增强单机上的αj点调度。这意味着提高了不相关机器的竞争比率,但也可能具有独立的利益。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信