Acta Mathematicae Applicatae Sinica

, Volume 11, Issue 3, pp 318–330

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


  • Yue Minyi 
    • Institute of Applied Mathematicsthe Chinese Academy of Science
  • Zhang Lei 
    • National Natural Science Foundation of China

DOI: 10.1007/BF02011198

Cite this article as:
Yue, M. & Zhang, L. Acta Mathematicae Applicatae Sinica (1995) 11: 318. doi:10.1007/BF02011198


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.

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