Abstract
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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References
D.S. Johnson. Near-Optimal Bin-Packing Algorithms. Doctoral Thesis, M.I.T., Cambridge, Mass. 1973.
B.S. Baker. A New Proof for the First-fit Decreasing Bin-Packing Algorithm.J. Algorithms, 1985, 6: 49–60.
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.
D.S. Johnson and M.R. Garey. A 71/60 Theorem for Bin-Packing.Journal of Complexity, 1985, 1: 65–106.
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This work is partly supported by the National Natural Science Foundation of China (No. 69074031).
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Yue, M., Zhang, L. A simple proof of the inequality MFFD(L)≤71/60 OPT(L) + 1,L for the MFFD bin-packing algorithm. Acta Mathematicae Applicatae Sinica 11, 318–330 (1995). https://doi.org/10.1007/BF02011198
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DOI: https://doi.org/10.1007/BF02011198