Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource

Peter Kling, Alexander Mäcker, Sören Riechers, Alexander Skopalik
{"title":"Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource","authors":"Peter Kling, Alexander Mäcker, Sören Riechers, Alexander Skopalik","doi":"10.1145/3087556.3087578","DOIUrl":null,"url":null,"abstract":"We consider a scheduling problem on m identical processors sharing an arbitrarily divisible resource. In addition to assigning jobs to processors, the scheduler must distribute the resource among the processors (e.g., for three processors in shares of 20%, 15%, and 65%) and adjust this distribution over time. Each job j comes with a size pj ∈ R and a resource requirement rj > 0. Jobs do not benefit when receiving a share larger than rj of the resource. But providing them with a fraction of the resource requirement causes a linear decrease in the processing efficiency. We seek a (non-preemptive) job and resource assignment minimizing the makespan. Our main result is an efficient approximation algorithm which achieves an approximation ratio of 2 + 1/(m-2). It can be improved to an (asymptotic) ratio of 1 + 1/(m-1) if all jobs have unit size. Our algorithms also imply new results for a well-known bin packing problem with splittable items and a restricted number of allowed item parts per bin. Based upon the above solution, we also derive an approximation algorithm with similar guarantees for a setting in which we introduce so-called tasks each containing several jobs and where we are interested in the average completion time of tasks (a task is completed when all its jobs are completed).","PeriodicalId":162994,"journal":{"name":"Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"798 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3087556.3087578","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9

Abstract

We consider a scheduling problem on m identical processors sharing an arbitrarily divisible resource. In addition to assigning jobs to processors, the scheduler must distribute the resource among the processors (e.g., for three processors in shares of 20%, 15%, and 65%) and adjust this distribution over time. Each job j comes with a size pj ∈ R and a resource requirement rj > 0. Jobs do not benefit when receiving a share larger than rj of the resource. But providing them with a fraction of the resource requirement causes a linear decrease in the processing efficiency. We seek a (non-preemptive) job and resource assignment minimizing the makespan. Our main result is an efficient approximation algorithm which achieves an approximation ratio of 2 + 1/(m-2). It can be improved to an (asymptotic) ratio of 1 + 1/(m-1) if all jobs have unit size. Our algorithms also imply new results for a well-known bin packing problem with splittable items and a restricted number of allowed item parts per bin. Based upon the above solution, we also derive an approximation algorithm with similar guarantees for a setting in which we introduce so-called tasks each containing several jobs and where we are interested in the average completion time of tasks (a task is completed when all its jobs are completed).
共享即关怀:共享资源的多处理器调度
考虑m个相同处理器共享任意可分资源的调度问题。除了将作业分配给处理器之外,调度器还必须在处理器之间分配资源(例如,三个处理器按20%、15%和65%的份额分配),并随着时间的推移调整这种分配。每个作业j的大小为pj∈R,资源需求为rj >0 0。当收到的资源份额大于rj时,作业不会受益。但是,为它们提供一小部分资源需求会导致处理效率的线性下降。我们寻求一个(非抢占式的)作业和资源分配,使最大完工时间最小化。我们的主要结果是一个有效的近似算法,它实现了近似比为2 + 1/(m-2)。如果所有作业都具有单位大小,则可以将其改进为1 + 1/(m-1)的(渐近)比率。我们的算法还暗示了一个众所周知的具有可分割物品和每个箱子允许的物品部件数量有限的垃圾箱包装问题的新结果。基于上述解决方案,我们还推导出一种近似算法,具有类似的保证设置,其中我们引入所谓的任务,每个任务包含几个任务,并且我们对任务的平均完成时间感兴趣(当所有任务完成时任务完成)。
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
自引率
0.00%
发文量
0
×
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:604180095
Book学术官方微信