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

A simple proof of the inequality FFD (L) ≤ 11/9 OPT (L) + 1, ∀L for the FFD bin-packing algorithm 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

Acta Mathematicae Applicatae Sinica , Volume 7 (4) – Jul 14, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009683
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References