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Parallel Simplex for Large Pure Network Problems: Computational Testing and Sources of Speedup

Author

Listed:
  • Richard S. Barr

    (Southern Methodist University, Dallas, Texas)

  • Betty L. Hickman

    (University of Nebraska at Omaha, Omaha, Nebraska)

Abstract

This paper reports on a new parallel implementation of the primal simplex method for minimum cost network flow problems that decomposes both the pivoting and pricing operations. The self-scheduling approach is flexible and efficient; its implementation is close in speed to the best serial code when using one processor, and is capable of substantial speedups as parallel computing units are added. An in-depth computational study of randomly generated transportation and transshipment problems verified the effectiveness of this approach, with results on a 20-processor 80386-based system that are competitive with, and occasionally superior to, massively parallel implementations using tens of thousands of processors. A microanalysis of the code's behavior identified unexpected sources of (the occasionally superlinear) speedup, including the evolutionary topology of the network basis.

Suggested Citation

  • Richard S. Barr & Betty L. Hickman, 1994. "Parallel Simplex for Large Pure Network Problems: Computational Testing and Sources of Speedup," Operations Research, INFORMS, vol. 42(1), pages 65-80, February.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:1:p:65-80
    DOI: 10.1287/opre.42.1.65
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    Citations

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    Cited by:

    1. Donghoon Lee & Matthew Wiswall, 2007. "A Parallel Implementation of the Simplex Function Minimization Routine," Computational Economics, Springer;Society for Computational Economics, vol. 30(2), pages 171-187, September.
    2. J. Hall, 2010. "Towards a practical parallelisation of the simplex method," Computational Management Science, Springer, vol. 7(2), pages 139-170, April.
    3. Robert E. Bixby & Alexander Martin, 2000. "Parallelizing the Dual Simplex Method," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 45-56, February.
    4. P. Beraldi & F. Guerriero & R. Musmanno, 1997. "Efficient Parallel Algorithms for the Minimum Cost Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 501-530, December.

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