Acta Mathematicae Applicatae Sinica

, Volume 11, Issue 3, pp 318–330 | Cite as

A simple proof of the inequality MFFD(L)≤71/60 OPT(L) + 1,L for the MFFD bin-packing algorithm

  • Yue Minyi 
  • Zhang Lei 


In 1985, Johnson and Garey[4] devised an algorithm which they call MFFD. Compared with other modifications of the famous FFD algorithm, their is apparently simpler in practical applications and substantially improves the worst case behavior of FFD. In fact, they proved that the inequality MFFD(L)≤71/60OPT(L)+31/6 holds for all the listsL. Their proof requires 40 pages. In this paper we give a proof for the inequality MFFD(L)≤71/60OPT(L)+1, ∀L. The proof is much simpler than theirs.

Key words

Bin-packing MFFD 


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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, 1985, 6: 49–60.Google Scholar
  3. [3]
    M. Yue. A Simple Proof of the Inequality FFD(L)≤11/9Opt(L)+1, ∀L for the FFD Bin-Packing Algorithm. Report No.90665-OR of the Forschungsinstitut Für Diskrete Mathematik, Universität Bonn, 1990.Google Scholar
  4. [4]
    D.S. Johnson and M.R. Garey. A 71/60 Theorem for Bin-Packing.Journal of Complexity, 1985, 1: 65–106.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1995

Authors and Affiliations

  • Yue Minyi 
    • 1
  • Zhang Lei 
    • 2
  1. 1.Institute of Applied Mathematicsthe Chinese Academy of ScienceBeijingChina
  2. 2.National Natural Science Foundation of ChinaBeijingChina

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