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Annals of Operations Research

, Volume 24, Issue 1, pp 233–259 | Cite as

On the exact upper bound for the multifit processor scheduling algorithm

  • Minyi Yue
Methodology

Abstract

We consider the well-known problem of schedulingn independent tasks nonpre-emptively onm identical processors with the aim of minimizing the makespan. Coffman, Garey and Johnson [1] described an algorithm, MULTIFIT, based on techniques from binpacking, with better worst performance than the LPT algorithm and proved that it satisfies a bound of 1.22. It has been claimed by Friesen [2] that this bound can be improved upon to 1.2. However, we found his proof, in particular his lemma 4.9, difficult to understand. Yue, Kellerer and Yu [3] have presented the bound 1.2 in a simpler way. In this paper, we prove first that the bound cannot exceed 13/11 and then prove that it is exactly 13/11.

Keywords

Schedule Algorithm Independent Task Identical Processor Processor Schedule Processor Schedule Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    E.G. Coffman, M.R. Garey and D.S. Johnson, An application of bin-packing to multiprocessor scheduling, SIAM J. Comput. 7(1978)1–17.Google Scholar
  2. [2]
    D.K. Friesen, Tighter bounds for the MULTIFIT processor scheduling algorithm, SIAM J. Comput. 13(1984)179–181.Google Scholar
  3. [3]
    M. Yue, H. Kellerer and Z. Yu, A simple proof of the inequalityR M(MF(k))≤1.2+1/2k in multiprocessor scheduling, Report No. 124, Institut für Mathematik, Technische Universität Graz (1988), pp. 1–10.Google Scholar
  4. [4]
    E.G. Coffman, Jr., etal., Approximation algorithms for bin-packing—an updated survey, in:Algorithm Design and Computer System Design, ed. G. Ausiello et al., CISM Courses and Lectures 284 (Springer, Vienna), pp. 49–106.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1990

Authors and Affiliations

  • Minyi Yue
    • 1
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijingP.R. China

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