A simple proof of the inequality FFD (L) ≤ 11/9 OPT (L) + 1, ∀L for the FFD bin-packing algorithm
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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 showed that for every listL, FFD(L)≤11/9OPT(L)+4. His proof required more than 100 pages. Later, Baker 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.
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