Acta Mathematicae Applicatae Sinica

, Volume 7, Issue 4, pp 321–331 | Cite as

A simple proof of the inequality FFD (L) ≤ 11/9 OPT (L) + 1, ∀L for the FFD bin-packing algorithm

  • Yue Minyi 


The first fit decreasing (FFD) heuristic algorithm is one of the most famous and most studied methods for an approximative solution of the bin-packing problem. For a listL, let OPT(L) denote the minimal number of bins into whichL can be packed, and let FFD(L) denote the number of bins used by FFD. Johnson[1] showed that for every listL, FFD(L)≤11/9OPT(L)+4. His proof required more than 100 pages. Later, Baker[2] gave a much shorter and simpler proof for FFD(L)≤11/9 OPT(L)+3. His proof required 22 pages. In this paper, we give a proof for FFD(L)≤11/9 OPT(L)+1. The proof is much simpler than the previous ones.


Approximative Solution Heuristic Algorithm Simple Proof Math Application 
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  1. [1]
    D.S. Johnson: Near-Optimal Bin-Packing Algorithms. Doctoral thesis, M.I.T., Cambridge, Mass., 1973.Google Scholar
  2. [2]
    B.S. Baker: A New Proof for the First-Fit Decreasing Bin-Packing Algorithm,J. Algorithms,6 (1985), 49–70.CrossRefGoogle Scholar
  3. [3]
    E.G. Coffman Jr., M.R. Garey and D.S. Johnson: An Application of Bin-Packing to Multiprocessor Scheduling,SIAM J. Comput,7 (1987), 1–17.CrossRefGoogle Scholar
  4. [4]
    Minyi Yue: On the Exact Upper Bound for the Multifit Processor Scheduling Algorithm,Operations Research in China (ed. Minyi Yue), 233–260,Ann. Oper. Res.,24 (1990).Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1991

Authors and Affiliations

  • Yue Minyi 
    • 1
    • 2
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijing
  2. 2.Forschungsinstitut für Diskrete MathematikBonn

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