Acta Mathematicae Applicatae Sinica

, Volume 7, Issue 4, pp 321–331

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

• Yue Minyi
Article

## Abstract

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.

## Keywords

Approximative Solution Heuristic Algorithm Simple Proof Math Application
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.

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## References

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.
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.
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

© 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