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Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime

Author

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  • Peruvemba Sundaram Ravi

    (School of Business and Economics, Wilfrid Laurier University)

  • Levent Tunçel

    (University of Waterloo)

  • Michael Huang

Abstract

In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime-optimal schedules, called the LD algorithm, has a simple worst-case performance bound: $$\frac{5m-2}{4m-1}$$ 5 m - 2 4 m - 1 , where m is the number of machines. We study the structure of potential minimal counterexamples to this conjecture, provide some new tools and techniques for the analysis of such algorithms, and prove that to verify the conjecture, it suffices to analyze the following case: for every $$m \ge 4$$ m ≥ 4 , $$n \in \{4m, 5m\}$$ n ∈ { 4 m , 5 m } , where n is the number of jobs.

Suggested Citation

  • Peruvemba Sundaram Ravi & Levent Tunçel & Michael Huang, 2016. "Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime," Journal of Scheduling, Springer, vol. 19(5), pages 547-561, October.
    • Handle: RePEc:spr:jsched:v:19:y:2016:i:5:d:10.1007_s10951-015-0467-4
    DOI: 10.1007/s10951-015-0467-4
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    References listed on IDEAS

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    1. E. G. Coffman & M. Yannakakis, 1984. "Permuting Elements Within Columns of a Matrix in Order to Minimize Maximum Row Sum," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 384-390, August.
    2. Brian Thomas Eck & Michael Pinedo, 1993. "On the Minimization of the Makespan Subject to Flowtime Optimality," Operations Research, INFORMS, vol. 41(4), pages 797-801, August.
    3. Johnny C. Ho & Johnny S. Wong, 1995. "Makespan minimization for m parallel identical processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 935-948, September.
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