{"title":"EPTAS for parallel identical machine scheduling with time restrictions","authors":"G. Jaykrishnan, Asaf Levin","doi":"10.1007/s10878-024-01108-y","DOIUrl":null,"url":null,"abstract":"<p>We consider the non-preemptive scheduling problem on identical machines where there is a parameter <i>B</i> and each machine in every unit length time interval can process up to <i>B</i> different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of <i>B</i>, and even the case of non-constant values of <i>B</i> on one machine was not known to admit a PTAS.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"8 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10878-024-01108-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of B, and even the case of non-constant values of B on one machine was not known to admit a PTAS.
我们考虑的是相同机器上的非抢占式调度问题，其中有一个参数 B，每台机器在每个单位长度的时间间隔内最多可以处理 B 个不同的作业。我们考虑的目标函数是最小化作业时间，并为这一问题开发了一种 EPTAS。在我们的研究之前，人们只知道在一台机器和 B 值恒定的情况下有一个 PTAS，甚至在一台机器上 B 值不恒定的情况下也不知道有一个 PTAS。
期刊介绍：
The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering.
The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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