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Parallel arc-allocation algorithms for optimizing generalized networks

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Abstract

Two parallel shared-memory algorithms are presented for the optimization of generalized networks. These algorithms are based on the allocation of arc-related operations in the (generalized) network simplex method. One method takes advantage of the multi-tree structure of basic solutions and performs pivot operations in parallel, utilizing locking to ensure correctness. The other algorithm utilizes only one processor for sequential pivoting, but parallelizes the pricing operation and overlaps this task with pivoting in a speculative manner (i.e. since pivoting and pricing involve data dependencies, a candidate for flow change generated by the pricing processors is not guaranteed to be acceptable, but in practice generally has this property). The relative performance of these two methods (on the Sequent Symmetry S81 multiprocessor) is compared and contrasted with that of a fast sequential algorithm on a set of large-scale test problems of up to 1,000,000 arcs.

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References

  1. D. Adolphson, Design of primal simplex generalized network codes using a preorder thread index, Working Paper, School of Management, Brigham Young University, Provo (1982).

    Google Scholar 

  2. R. Barr, F. Glover and D. Klingman, Enhancements of spanning tree labeling procedures for network optimization, INFOR 17(1979)16–34.

    Google Scholar 

  3. G.G. Brown and R.D. McBride, Solving generalized networks, Manag. Sci. 30(1984)1497–1523.

    MathSciNet  Google Scholar 

  4. M. Chang, M. Engquist, R. Finkel and R. Meyer, A parallel algorithm for generalized networks, Ann. Oper. Res. 14(1988)125–145.

    Google Scholar 

  5. M. Chang and M. Engquist, On the number of quasi-trees in an optimal generalized network basis, COAL Newsletter 14(1986)5–9.

    Google Scholar 

  6. R. Clark and R. Meyer, Multiprocessor algorithms for generalized network flows, Technical Report No. 739, Department of Computer Sciences, The University of Wisconsin-Madison (1987).

  7. M. Engquist and M. Chang, New labeling procedures for the basis graph in generalized network, Oper. Res. Lett. 4, 4(1985)151–155.

    Article  Google Scholar 

  8. F. Glover, D. Klingman and J. Stutz, Extension of the augmented predecessor index method to generalized network problems, Transportation Science 7(1973)377–384.

    Article  Google Scholar 

  9. F. Glover, D. Karney, D. Klingman and A. Napier, A computation study on start procedures, basis change criteria, and solution algorithms for transportation problems, Manag. Sci. 20(1974)793–813.

    Google Scholar 

  10. F. Glover, J. Hultz, D. Klingman and J. Stutz, Generalized networks: A fundamental planning tool, Manag. Sci. 24(1984)1209–1220.

    Google Scholar 

  11. M. Grigoriadis, An efficient implementation of the network simplex method, Math. Progr. Study 26(1984)83–111.

    Google Scholar 

  12. P. Jensen and J.W. Barnes,Network Flow Programming (Wiley, New York, 1980).

    Google Scholar 

  13. J. Kennington and R. Helgason,Algorithms for Network Flow Programming (Wiley, New York, 1980).

    Google Scholar 

  14. J. Kennington and R. Muthukrishnan, Solving generalized network problems on a shared memory multiprocessor, Technical Report 88-OR-21, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (1988).

    Google Scholar 

  15. D. Klingman, A. Napier and J. Stutz, NETGEN: A program for generating large scale capacitated assignment, transportation, and minimum cost flow problems, Manag. Sci. 20(1974)814–821.

    Google Scholar 

  16. B. Murtagh and M. Saunders, Large-scale linearly constrained optimization, Math. Progr. 14(1978)41–72.

    Article  Google Scholar 

  17. J. Peters, A parallel algorithm for minimal cost network flow problems, Technical Report No. 762, Department of Computer Sciences, The University of Wisconsin-Madison (1988).

  18. J. Peters, The network simplex method on a multi-processor (June 1988).

  19. S. Zenios, Sequential and parallel algorithms for convex generalized network problems and related applications, Ph.D. Thesis, Civil Engineering Department, Princeton University, Princeton, NJ (1986).

    Google Scholar 

  20. S. Zenios and J. Mulvey, A distributed algorithm for convex network optimization problems, Report EES-85-10, Engineering-Management Systems, Civil Engineering Department, Princeton University, Princeton, NJ (1985).

    Google Scholar 

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Authors and Affiliations

  1. Computer Sciences Department and Center for the Mathematical Sciences, The University of Wisconsin-Madison, 53706, Madison, Wisconsin, USA

    R. H. Clark & R. R. Meyer

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  1. R. H. Clark
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  2. R. R. Meyer
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This research was supported in part by NSF grant CCR-8709952 and AFOSR grant AFOSR-86-0194.

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Clark, R.H., Meyer, R.R. Parallel arc-allocation algorithms for optimizing generalized networks. Ann Oper Res 22, 129–160 (1990). https://doi.org/10.1007/BF02023051

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