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An upper bound for the speedup of parallel best-bound branch-and-bound algorithms

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Abstract

This paper derives an upper bound for the speedup obtainable by any parallel branch-and-bound algorithm using the best-bound search strategy. We confirm that parallel branch-and-bound can achieve nearly linear, or even super-linear, speedup under the appropriate conditions.

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References

  1. A. M. Geoffrion and R. E. Marsten,Integer programming algorithms: a framework and state of the art survey, Management Science, 18, 9 (May 1972), 465–491.

    Google Scholar 

  2. M. Held and R. Karp,The traveling salesman problem and minimum spanning trees: Part II, Mathematical Programming, 1, 1 (October 1971), 6–25.

    Article  Google Scholar 

  3. T. Ibaraki,Theoretical comparisons of search strategies in branch-and-bound algorithms, Internat. Journal of Computer and Information Sciences, 5, 4 (1976), 315–344.

    Article  Google Scholar 

  4. E. Ignall and L. Schrage,Application of branch and bound technique to some flow-shop scheduling problems, Operations Research, 13, 3 (May–June 1965), 400–412.

    Google Scholar 

  5. T.-H. Lai and S. Sahni,Anomalies in parallel branch-and-bound algorithms, Proc. 1983 Internat. Conf. on Parallel Processing, 183–190.

  6. G.-J. Li and B. W. Wah,Computational efficiency of parallel approximate branch-and-bound algorithms, Proc. 1984 Internat. Conf. on Parallel Processing, 473–480.

  7. J. D. C. Little, K. G. Murty, D. W. Sweeney, and C. Karel,An algorithm for the traveling salesman problem, Operations Research 11,6 (November–December 1963), 972–989.

    Google Scholar 

  8. J. Mohan,Experience with two parallel programs solving the traveling salesman problem, Proc. 1983 Internat. Conf. on Parallel Processing, 191–193.

  9. N. J. Nilsson,Principles of Artificial Intelligence, Tioga Publishing Co., Palo Alto, CA, 1980, Section 2.4.

    Google Scholar 

  10. J. F. Pierce and W. B. Crowston,Tree-search algorithms for quadratic assignment problems, Naval Research Logistics Quarterly, 18, 1 (March 1971), 1–36.

    Google Scholar 

  11. L. Schrage,Solving resource-constrained network problems by implicit enumeration-nonpreemptive case, Operations Research, 18, 2 (March–April 1970), 263–278.

    Google Scholar 

  12. L. Schrage,Solving resource-constrained network problems by implicit enumeration-preemptive case, Operations Research, 20, 3 (May–June 1972), 668–677.

    Google Scholar 

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This work was supported by U.S. Army Research Office grant DAAG29-82-K-0107.

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Quinn, M.J., Deo, N. An upper bound for the speedup of parallel best-bound branch-and-bound algorithms. BIT 26, 35–43 (1986). https://doi.org/10.1007/BF01939360

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  • DOI: https://doi.org/10.1007/BF01939360

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