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Efficient Polynomial Time Approximation Scheme for Scheduling Jobs onUniform Processors

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  • First Online:
Encyclopedia of Algorithms

  • 194 Accesses

Years and Authors of Summarized Original Work

  • 2009; Jansen

  • 2011; Jansen, Robenek

  • 2014; Chen, Jansen, Zhang

Problem Definition

We consider the following fundamental problem in scheduling theory. Suppose that there is a set \(\mathcal{J}\) of n independent jobs J j with processing time p j and a set \(\mathcal{P}\) of m nonidentical processors P i that run at different speeds s i . If job J j is executed on processor P i , then processor P i needs \(p_{j}/s_{i}\) time units to complete the job. The goal is to find an assignment \(a : \mathcal{J} \rightarrow \mathcal{P}\) for the jobs to the processors that minimizes the total length of the schedule \(\max _{i=1,\ldots ,m}\sum _{J_{j}:a(J_{j})=P_{i}}p_{j}/s_{i}\). This is the minimum time needed to complete all jobs on the processors. The problem is denoted Q | | Cmax and it is also called the minimum makespan problem on uniform parallel processors. By simplicity we may assume that the number mof processors is bounded by the number of...

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Authors and Affiliations

  1. Department of Computer Science, University of Kiel, Kiel, Germany

    Klaus Jansen

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  1. Klaus Jansen
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Correspondence to Klaus Jansen .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Jansen, K. (2016). Efficient Polynomial Time Approximation Scheme for Scheduling Jobs onUniform Processors. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_500

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