Online and Semi-online Scheduling

Tan, Zhiyi; Zhang, An

doi:10.1007/978-1-4419-7997-1_2

Cited by 20 publications

(7 citation statements)

References 171 publications

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“…In the literature (cf., e.g., Tan and Zhang 2013), two basic models of online scheduling are discussed: 1) online "over list" model and 2) online "over time" one. In online "over list" scheduling, it is assumed that jobs come into the system one after another, i.e., the information on the next job becomes available-without any delay-after the previous one has been processed .…”

Section: Online Problem P|d J = D Onl I Ne Over L I St|ymentioning

confidence: 99%

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Chen

Sterna

Han

et al. 2015

J Sched

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In the paper, we consider the problem of scheduling jobs on parallel identical machines with the late work criterion and a common due date, both offline and online cases. Since the late work criterion has not been studied in the online mode so far, the analysis of the online problem is preceded by the analysis of the offline problem, whose complexity status has not been formally stated in the literature yet. Namely, for the offline mode, we prove that the twomachine problem is binary NP-hard, and the general case is unary NP-hard. In the online mode we assume that jobs arrive in the system one by one, i.e., we consider the online over list model. We give an algorithm with a competitive ratio being a function of the number of machines, and we prove the optimality of this approach for two identical machines.

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Section: Online Problem P|d J = D Onl I Ne Over L I St|ymentioning

confidence: 99%

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Chen

Sterna

Han

et al. 2015

J Sched

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“…[42] 3+ √ 17 4 [42] 助下获得了证实 (参见文献 [38,40]), 而 P 3|decr|C max 是目前 m > 2 且为固定数时唯一得到最好算法的问题. 两台同型机半在线问题成果更为丰富, 且绝大多数已得到最好算法, 相关结果可参见文献 [6].…”

Section: 已知部分信息的半在线排序问题unclassified

“…图 1 给出了两台同类机在线和半在线问题的参数最好算法竞争比图像, 以及与 UB&LB 有关的同型机和有等级同型机参数最好算法竞争比图像. 有等级同型机的其他半在线结果参见表 2 和文献 [6].…”

Section: 特殊加工机制下的在线排序问题unclassified

Online scheduling on parallel machines: A survey

Ling¹,

Tan²

2020

Sci. Sin.-Math.

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关键词排序在线竞争比 MSC (2010) 主题分类 90B35, 90C27 1 引言在线问题 (online problem) 是 20 世纪 80 年代起逐渐形成的一个新的研究方向, 可用于求解在线问题的算法称为在线算法 (online algorithm). 在线的两个基本特征是实例信息随算法执行过程逐渐披露、以及算法决策不可因后续出现的信息而更改. 相应地, 实例信息在算法执行前全部已知的问题称为离线问题 (offline problem). 在线问题及算法可抽象为在算法设计者和对手 (adversary) 之间进行的一个需求-应答博弈 (request-answer game). 对手每给出一个需求, 算法根据此前双方的应对和当前需求决定如何应答, 而对手再根据至目前为止双方的应对给出下一个需求. 算法的目标是使其性能尽可能好, 而对手的目标则恰好相反. 为对一个在线算法求解在线问题的性能作出定量的评估, 最坏情况比被移植到在线问题的研究中, 并结合其特点称其为竞争比 (competitive ratio). 称 ρ = inf{r 1 | C A (I) rC * (I), ∀ I} (ρ = inf{r 1 | C * (I) rC A (I), ∀ I})

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“…For a more detailed overview of the literature on online and various semionline variants, we refer to the survey of Tan and Zhang [24].…”

Section: Survey Of the Literaturementioning

confidence: 99%

Tight lower bounds for semi-online scheduling on two uniform machines with known optimum

Dósa

Fügenschuh

Tan

et al. 2018

Cent Eur J Oper Res

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We consider a semi-online version of the problem of scheduling a sequence of jobs of different lengths on two uniform machines with given speeds 1 and s. Jobs are revealed one by one (the assignment of a job has to be done before the next job is revealed), and the objective is to minimize the makespan. In the considered variant the optimal offline makespan is known in advance. The most studied question for this online-type problem is to determine the optimal competitive ratio, that is, the worst-case ratio of the solution given by an algorithm in comparison to the optimal offline solution. In this paper, we make a further step towards completing the answer to this question by determining the optimal competitive ratio for s between 5+ √ 241 12 ≈ 1.7103 and √ 3 ≈ 1.7321, one of the intervals that were still open. Namely, we present and analyze a compound algorithm achieving the previously known lower bounds.

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Online and Semi-online Scheduling

Cited by 20 publications

References 171 publications

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Online scheduling on parallel machines: A survey

Tight lower bounds for semi-online scheduling on two uniform machines with known optimum

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