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Scheduling Problems in a Practical Allocation Model

Author

Listed:
  • Lisa Hollermann

    (IBM Corporation)

  • Tsan-sheng Hsu

    (Institute of Information Science, Academia Sinica, Nankang)

  • Dian Rae Lopez

    (University of Minnesota)

  • Keith Vertanen

    (Linkvping Universitet)

Abstract

A parallel computational model is defined which addresses I/O contention,latency, and pipe-lined message passing between tasks allocated to differentprocessors. The model can be used for parallel task-allocation on either anetwork of workstations or on a multi-stage inter-connected parallel machine.To study performance bounds more closely, basic properties are developed forwhen the precedence constraints form a directed tree. It is shown that theproblem of optimally scheduling a directed one-level precedence tree on anunlimited number of identical processors in this model is NP-hard. Theproblem of scheduling a directed two-level precedence tree is also shown tobe NP-hard even when the system latency is zero. An approximation algorithm is then presented for scheduling directedone-level task trees on an unlimited number of processors with anapproximation ratio of 3. Simulation results show that this algorithm is, infact, much faster than its worst-case performance bound. Better simulationresults are obtained by improving our approximation algorithm usingheusistics. Restricting the problem to the case of equal task executiontimes, a linear-time algorithm is presented to find an optimal schedule.

Suggested Citation

  • Lisa Hollermann & Tsan-sheng Hsu & Dian Rae Lopez & Keith Vertanen, 1997. "Scheduling Problems in a Practical Allocation Model," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 129-149, June.
    • Handle: RePEc:spr:jcomop:v:1:y:1997:i:2:d:10.1023_a:1009799631608
    DOI: 10.1023/A:1009799631608
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    References listed on IDEAS

    as
    1. J. Y. Colin & P. Chrétienne, 1991. "C.P.M. Scheduling with Small Communication Delays and Task Duplication," Operations Research, INFORMS, vol. 39(4), pages 680-684, August.
    2. Cheng, T. C. E. & Sin, C. C. S., 1990. "A state-of-the-art review of parallel-machine scheduling research," European Journal of Operational Research, Elsevier, vol. 47(3), pages 271-292, August.
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