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

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 list L, let OPT(L) denote the minimal number of bins into which L can be packed, and let FFD(L) denote the number of bins used by FFD. Johnson[1] showed that for every list L, 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. © 1991 Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.