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


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.


Schedule Algorithm Independent Task Identical Processor Processor Schedule Processor Schedule Algorithm 
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  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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