We consider the problem of scheduling jobs online nonclairvoyantly, that is, when job sizes are not known Our focus is on minimizing mean slowdown, defined as the ratio of flow time to the size of the job We use resource augmentation in terms of allowing a faster processor to the online algorithm to make up for its lack of knowledge of job sizesOur main result is an O(1)-speed O(log2 B)-competitive algorithm for minimizing mean slowdown non-clairvoyantly, when B is the ratio between the largest and smallest job sizes On the other hand, we show that any O(1)-speed algorithm, deterministic or randomized, is at least ?(logB) competitiveThe motivation for bounded job sizes is supported by an ?(n) lower bound for arbitrary job sizes, where n is the number of jobs Furthermore, a lower bound of ?(B) justifies the need for resource augmentation even with bounded job sizes For the static case, ie when all jobs arrive at time 0, we give an O(logB) competitive algorithm which does not use resource augmentation and a matching ?(logB) lower bound on the competitiveness

Non-clairvoyant scheduling for minimizing mean slowdown

In real-life applications, neither all the inputs of an algorithm are available at the outset, as in an offline framework, nor do they occur one by one in order, as in an online setup. Semi-online is an intermediate theoretically and practically significant framework with additional information on the successive inputs to address the limitations of online and offline frameworks. One key motivation for studying semi-online algorithms is to investigate how additional information can improve the performance of online algorithms. In online scheduling, jobs are received one by one and each job must be scheduled irrevocably before the availability of the next job. Semi-online scheduling is a relaxed variant of online scheduling, where some Extra Piece Information (EPI) about the whole job sequence is known a priori, or additional algorithmic extensions are allowed. The EPI may include one or more of the following parameter(s) such as the maximum processing time, the total sum of the processing time of all jobs, arrival sequence of the jobs based on processing time, optimum makespan value, or the range of processing time. The design of improved competitive semi-online algorithms for m-machine scheduling problem has received significant research attention after the seminal works of Liu et al. (1996) and Kellerer et al. (1997). In this survey article, we highlight the scholarly contributions and state-of-the-art results for semi-online scheduling on parallel machine models such as identical, uniformly related, and unbounded batch by considering preemptive and non-preemptive as the processing formats with optimality criteria such as makespan, load balancing, machine cost, Lp-norm load balancing, early work maximization, and the sum of completion time plus total penalty cost. The survey begins with a brief introduction to the online and semi-online frameworks for the m-machine scheduling problem and presentation of a standard well-known algorithmic performance measure, the competitive analysis. Practical applications, preliminary concepts, research motivation, and taxonomy of semi-online scheduling are presented as a foundation for a basic understanding of the area. State-of-the-art results achieved by the deterministic semi-online algorithms are classified and presented based on machine models and known EPI with a special focus on novel intuitions and algorithmic development. We discuss and analyze the impact of EPI on the competitive performance of semi-online algorithms. A classification of the references based on specific EPI is outlined for further research investigation. Finally, we conclude the survey with non-trivial research challenges and open problems. 

/pdf/semi-online-scheduling-a-survey-1lowuqiq.pdf

Semi-online scheduling: A survey

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.

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

This paper investigates an online hierarchical scheduling problem with resource augmentation, i.e., the resources of the online algorithms are different from those of the offline algorithms. The machines are provided with different capacity according to their hierarchies. One with the hierarchy 1 has a speed of s (q) in the online (offline) algorithms and can process all the jobs. The other with hierarchy 2 has a speed of 1 in the online/offline algorithms and can only process partial jobs. The objective is to minimize makespan. For any 0 < q,s < 8, we present optimal online algorithms with parametric competitive ratios.

Optimal online algorithms on two hierarchical machines with resource augmentation

This paper investigates an online hierarchical scheduling problem with resource augmentation, ie, the resources of the online algorithms are different from those of the offline algorithms The machines are provided with different capacity according to their hierarchies One with the hierarchy 1 has a speed of s(q) in the online (offline) algorithms and can process all the jobs The other with hierarchy 2 has a speed of 1 in the online/offline algorithms and can only process partial jobs The objective is to minimize makespan For any 0 < q, s < ∞, we present optimal online algorithms with parametric competitive ratios

We study the problem of on-line scheduling on two uniformly related machines where the on-line algorithm has resources different from those of the off-line algorithm. We consider three versions of this problem, preemptive semi-online, non-preemptive on-line and preemptive on-line scheduling. For all these cases we design algorithms with best possible competitive ratios as functions of the machine speeds.

/pdf/optimal-on-line-algorithms-to-minimize-makespan-on-two-4w9d33nd1r.pdf

Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation

We study the problem of on-line scheduling on two uniformly related machines where the on-line algorithm has resources different from those of the off-line algorithm We consider three versions of this problem: preemptive semi-online, non-preemptive on-line and preemptive on-line scheduling For all these cases we design algorithms with best possible competitive ratios as a function of the machine speeds

/pdf/optimal-on-line-algorithms-to-minimize-makespan-on-two-2wjfkm0gs2.pdf

Optimal on-line algorithms to minimize makespan on two machines with resource augmentation

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Arik Ganot

Author Tools

Chat about Author

Papers

Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation

Optimal on-line algorithms to minimize makespan on two machines with resource augmentation