Abstract
The bin packing problem is to pack a list of reals in (0, 1] into unit-capacity bins using the minimum number of bins. LetR∞[A] be the limiting worst value for the ratioA(L)/OPT(L) asOPT(L) goes to ∞, whereA(L) denotes the number of bins used when the approximation algorithmA is applied to the listL, andOPT(L) denotes the minimum number of bins needed to packL. For Best-k-Fit (BkF for short,k≥1), we prove in this paper thatR∞[BkF]=1.7+3/10k.
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