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Improved Algorithms for Online Scheduling of Malleable Parallel Jobs on Two Identical Machines

Author

Listed:
  • Hao Zhou

    (Department of Basic Science, Zhejiang Shuren University, Hangzhou 310015, P. R. China)

  • Ping Zhou

    (School of Humanities, Zhejiang Business College, Hangzhou 310053, P. R. China)

  • Yiwei Jiang

    (Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China)

Abstract

This paper addresses online scheduling of malleable parallel jobs to minimize the maximum completion time, i.e., makespan. It is assumed that the execution time of a job Jj with processing time pj is pj/k + (k-1)c if the job is assigned to k machines, where c > 0 is a constant setup time. We consider online algorithms for the scheduling problem on two identical machines. Namely, the job Jj can be processed on one machine with execution time pj or alternatively two machines in parallel with execution time pj/2+c. For the asymptotical competitive ratio, we provide an improved online algorithm with makespan no more than (3/2)C* +c/2, where C* is the optimal makespan. For the strict competitive ratio, we propose an online algorithm with competitive ratio of 1.54, which is close to the lower bound of 1.5.

Suggested Citation

  • Hao Zhou & Ping Zhou & Yiwei Jiang, 2015. "Improved Algorithms for Online Scheduling of Malleable Parallel Jobs on Two Identical Machines," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-13.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:05:n:s0217595915500347
    DOI: 10.1142/S0217595915500347
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