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Online Preemptive Scheduling on Parallel Machines

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Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2009; Ebenlendr, Jawor, Sgall

  • 2010; Ebenlendr

  • 2011; Ebenlendr, Sgall

Problem Definition

We consider an online version of the classical problem of preemptive scheduling on uniformly related machines.

We are given m machines with speeds s1 ≥ s2 ≥ … ≥ s m and a sequence of jobs, each described by its processing time (length). The actual time needed to process a job with length p on a machine with speed s is p∕s. In the preemptive version, each job may be divided into several pieces, which can be assigned to different machines in disjoint time slots. (A job may be scheduled in several time slots on the same machine, and there may be times when a partially processed job is not running at all.) The objective is to find a schedule of all jobs in which the maximal completion time (makespan) is minimized.

In the online problem, jobs arrive one by one and the algorithm needs to assign each incoming job to some time slots on some machines, without...

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Recommended Reading

  1. Berman P, Charikar M, Karpinski M (2000) On-line load balancing for related machines. J. Algorithms 35:108–121

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  2. Ebenlendr T (2010) Semi-online preemptive scheduling: study of special cases. In: Proceedings of 8th international conference on parallel processing and applied mathematics (PPAM 2009), part II, Wroclaw. Lecture notes in computer science, vol 6068. Springer, pp 11–20

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  3. Ebenlendr T (2011) Combinatorial algorithms for online problems: semi-online scheduling on related machines. Ph.D. thesis, Charles University, Prague

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  4. Ebenlendr T, Jawor W, Sgall J (2009) Preemptive online scheduling: optimal algorithms for all speeds. Algorithmica 53:504–522

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  6. Ebenlendr T, Sgall J (2011) Semi-online preemptive scheduling: one algorithm for all variants. Theory Comput Syst 48:577–613

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Author information

Authors and Affiliations

  1. Computer Science Institute, Charles University, Prague, Czech republic

    Jiřı́ Sgall

Authors
  1. Jiřı́ Sgall
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Corresponding author

Correspondence to Jiřı́ Sgall .

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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Sgall, J. (2016). Online Preemptive Scheduling on Parallel Machines. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_501

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