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Optimal On-Line Scheduling of Parallel Jobs with Dependencies

Author

Listed:
  • Anja Feldmann

    (Carnegie Mellon University)

  • Ming-Yang Kao

    (Duke University)

  • Jiří Sgall

    (Mathematical Institute)

  • Shang-Hua Teng

    (University of Minnesota)

Abstract

We study the following general on-line scheduling problem. Paralleljobs arrive on a parallel machine dynamically according to thedependencies between them. Each job requests a certain number ofprocessors in a specific communication configuration, but its runningtime is not known until it is completed. We present optimal on-linealgorithms for PRAMs and one-dimensional meshes, and efficientalgorithms for hypercubes and general meshes. For PRAMs we obtainoptimal tradeoffs between the competitive ratio and the largestnumber of processors requested by any job. Our results demonstrate that on-line scheduling with dependenciesdiffers from scheduling without dependencies in several crucialaspects. First, it is essential to use virtualization, i.e., toschedule parallel jobs on fewer processors than requested. Second,the maximal number of processors requested by a job has significantinfluence on the performance. Third, the geometric structure of thenetwork topology is an even more important factor than in the absenceof dependencies.

Suggested Citation

  • Anja Feldmann & Ming-Yang Kao & Jiří Sgall & Shang-Hua Teng, 1998. "Optimal On-Line Scheduling of Parallel Jobs with Dependencies," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 393-411, December.
    • Handle: RePEc:spr:jcomop:v:1:y:1998:i:4:d:10.1023_a:1009794729459
    DOI: 10.1023/A:1009794729459
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    References listed on IDEAS

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    1. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Complexity of Scheduling under Precedence Constraints," Operations Research, INFORMS, vol. 26(1), pages 22-35, February.
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    Cited by:

    1. Vredeveld, T., 2009. "Stochastic Online Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Havill, Jessen T. & Mao, Weizhen, 2008. "Competitive online scheduling of perfectly malleable jobs with setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1126-1142, June.

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