Semi-online scheduling with combined information on two identical machines in parallel

Cao, Qian; Wan, Guohua

doi:10.1007/s10878-014-9778-1

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…Cao et al [11] obtained a tight bound of 1.2 by considering Max and the value of the optimum makespan as the known EPI. Cao and Wan [12] considered the known information on Decr and T GRP (1, r) and proved a tight bound of 1.16 on the competitive ratio. We now present a summary of the best known competitive bounds in Table 2.…”

Section: State-of-the-art Resultsmentioning

confidence: 99%

New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines

Dwibedy¹,

Mohanty²

2021

Preprint

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Design and analysis of constant competitive deterministic semi-online algorithms for the multi-processor scheduling problem with small number of identical machines have gained significant research interest in the last two decades. In the semi-online scheduling problem for makespan minimization, we are given a sequence of independent jobs one by one in order and upon arrival, each job must be allocated to a machine with prior knowledge of some Extra Piece of Information (EPI) about the future jobs. Researchers have designed multiple variants of semi-online scheduling algorithms with constant competitive ratios by considering one or more EPI. In this paper, we propose four new variants of competitive deterministic semi-online algorithms for smaller number of identical machines by considering two EPI such as Decr and Sum. We obtain improved upper bound and lower bound results on the competitive ratio for our proposed algorithms, which are comparable to the best known results in the literature. In two identical machines setting with known Sum, we show a tight bound of 1.33 on the competitive ratio by considering a sequence of equal size jobs. In the same setting we achieve a lower bound of 1.04 and an upper bound of 1.16 by considering Sum and a sequence of jobs arriving in order of decreasing sizes. For three identical machines setting with known Decr and Sum, we show a lower bound of 1.11 on the competitive ratio. In this setting, we obtain an upper bound of 1.5 for scheduling a sequence of equal size jobs and achieves an upper bound of 1.2 by considering a sequence of decreasing size jobs. Further we develop an improved competitive algorithm with an upper bound of 1.11 on the competitive ratio.

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Section: State-of-the-art Resultsmentioning

confidence: 99%

New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines

Dwibedy¹,

Mohanty²

2021

Preprint

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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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“…Secondly, they obtained a LB of 1.11 with known Sum and Decr. Recent contributions in this setting are due to [108][109][110][111][112][113]. Important results achieved in the literature for online scheduling with combined EPI s are reported in Table 14.…”

Section: Arrival Sequence Of the Jobsmentioning

confidence: 99%

Online Scheduling with Makespan Minimization: State of the Art Results, Research Challenges and Open Problems

Dwibedy,

Mohanty

2020

Preprint

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Online scheduling has been a well studied and challenging research problem over the last five decades since the pioneering work of Graham with immense practical significance in various applications such as interactive parallel processing, routing in communication networks, distributed data management, client-server communications, traffic management in transportation, industrial manufacturing and production. In this problem, a sequence of jobs is received one by one in order by the scheduler for scheduling over a number of machines. On arrival of a job, the scheduler assigns the job irrevocably to a machine before the availability of the next job with an objective to minimize the completion time of the scheduled jobs. This paper highlights the state of the art contributions for online scheduling of a sequence of independent jobs on identical and uniform related machines with a special focus on preemptive and non-preemptive processing formats by considering makespan minimization as the optimality criterion. We present the fundamental aspects of online scheduling from a beginner's perspective along with a background of general scheduling framework. Important competitive analysis results obtained by well-known deterministic and randomized online scheduling algorithms in the literature are presented along with research challenges and open problems. Two of the emerging recent trends such as resource augmentation and semi-online scheduling are discussed as a motivation for future research work.

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Semi-online scheduling with combined information on two identical machines in parallel

Cited by 5 publications

References 7 publications

New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines

New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines

Online scheduling on parallel machines: A survey

Online Scheduling with Makespan Minimization: State of the Art Results, Research Challenges and Open Problems

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