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MapReduce machine covering problem on a small number of machines

Author

Listed:
  • Yiwei Jiang

    (Zhejiang Gongshang University)

  • Ping Zhou

    (Zhejiang Business College)

  • Wei Zhou

    (Zhejiang Sci-Tech University)

Abstract

We study machine covering problem in MapReduce system. Each job consists of two sets of tasks, namely the map tasks and reduce tasks. A job’s reduce tasks can only be processed after all its map tasks are finished. The map tasks are fractional, i.e., they can be arbitrarily split and processed on different machines in parallel. Our goal is to maximize the minimum machine completion time. We consider two variants of the problem, namely the cases involving preemptive reduce tasks and non-preemptive reduce tasks. For preemptive reduce tasks, we present optimal solution algorithms for the problem on two and three machines. For non-preemptive reduce tasks, we provide an approximation algorithm with a tight worse-case ratio of $$\frac{4}{3}$$ 4 3 for the problem on two machines.

Suggested Citation

  • Yiwei Jiang & Ping Zhou & Wei Zhou, 2019. "MapReduce machine covering problem on a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1066-1076, November.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:4:d:10.1007_s10878-019-00436-8
    DOI: 10.1007/s10878-019-00436-8
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    References listed on IDEAS

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    1. Yiwei Jiang & Zhiyi Tan & Yong He, 2005. "Preemptive Machine Covering on Parallel Machines," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 345-363, December.
    2. Cong Chen & Yinfeng Xu & Yuqing Zhu & Chengyu Sun, 2017. "Online MapReduce scheduling problem of minimizing the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 590-608, February.
    3. Yiwei Jiang & Wei Zhou & Ping Zhou, 2018. "An Optimal Preemptive Algorithm for Online MapReduce Scheduling on Two Parallel Machines," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-11, June.
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    1. Yiwei Jiang & Wei Zhou & Ping Zhou, 2018. "An Optimal Preemptive Algorithm for Online MapReduce Scheduling on Two Parallel Machines," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-11, June.
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