Advertisement

Determining the Performance Ratio of Algorithm Multifit for Scheduling

  • Feng Cao
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 4)

Abstract

Scheduling n independent tasks nonpreemptively on m identical processors with the aim of minimizing the makespan is well-known to be NP-complete. Coffman, Garey and Johnson [1] described an algorithm-MULTIFIT and proved that it satisfies a bound of 1.22. Friesen [2] showed an example in which the upper bound is no less than 13/11. Yue, Keller and Yu proved an upper bound of 1.2. Yue gave a proof for the upper bound of 13/11, but the proof missed some casesIn this paper, a complete and simple proof is presented.

Keywords

Type Item Performance Ratio Small Item Independent Task Extra Weight 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E.G.Coffman, M.R.Gray and D.J.Johnson, An application of bin-packing to multiprocessor scheduling, SIAM Journal of Computation, 7(1978)1–17MATHCrossRefGoogle Scholar
  2. 2.
    D.K.Friesen, Tighter bounds for the MULTIFIT processor scheduling algorithm, SIAM Journal of Computation, 13(1984)179–181MathSciNetCrossRefGoogle Scholar
  3. 3.
    M.Yue, H Kellerer and Z.Yu, A simple proof of the inequalityRM(MF(k))≤1.2 + (1/2)k in multiprocessor scheduling, Report NO.124, Institut fur Mathematik, Technische Universitat Graz(1988), pp. 1–10.Google Scholar
  4. 4.
    M.Yue, On the exact upper bound for the MULTIFIT processor scheduling algorithm, Annals of Operation Research, 24(1990)233–250MATHCrossRefGoogle Scholar
  5. 5.
    E.G.Coffman, Jr., et al., Approximation algorithms for bin-packing-an updated survey, Algorithm Design and Computer System Design, (eds.) G.Ausiello et al., CISM Courses and Lectures 284(Springer, Vienna), pp. 49–106.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Feng Cao
    • 1
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolisUSA

Personalised recommendations