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Online C-benevolent job scheduling on multiple machines

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Abstract

We consider scheduling a sequence of C-benevolent jobs on multiple homogeneous machines. For two machines, we propose a 2-competitive Cooperative Greedy algorithm and provide a lower bound of 2 for the competitive ratio of any deterministic online scheduling algorithms on two machines. For multiple machines, we propose a Pairing-m Greedy algorithm, which is deterministic 2-competitive for even number of machines and randomized \((2+2/{\hbox {m}})\)-competitive for odd number of machines. We provide a lower bound of 1.436 for the competitive ratio of any deterministic online scheduling algorithms on three machines, which is the best known lower bound for competitive ratios of deterministic scheduling algorithms on three machines.

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Acknowledgements

This research has been supported in part by the Air Force Office of Scientific Research under Grant No. FA9550-15-1-0100. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Government, or the Air Force Office of Scientific Research.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Ge Yu

  2. Department of Computer Science, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Sheldon H. Jacobson

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  1. Ge Yu
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  2. Sheldon H. Jacobson
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Correspondence to Ge Yu.

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Yu, G., Jacobson, S.H. Online C-benevolent job scheduling on multiple machines. Optim Lett 12, 251–263 (2018). https://doi.org/10.1007/s11590-017-1191-0

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  • DOI: https://doi.org/10.1007/s11590-017-1191-0

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