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.
deZusammenfassung
Das Bin-Packing-Problem besteht darin, eine Liste von reellen Zahlen aus (0, 1], in Kästen (“bins”) der Kapazität 1 zu verpacken. SeiA(L) die Zahl der Kästen, die benötigt wird, wenn der ApproximationsalgorithmusA auf die ListeL angewandt wird undOPT(L) die Minimalzahl der für das Packen vonL benötigten Kästen. Sei weiterR ∞[A] der Grenzwert des VerhältnissesA(L)/OPT(L) für OPT(L)→∞ im ungünstigsten Fall. Für Best-k-Fit (kurzBkF,k≥1) zeigen wir in diesem Beitrag, daßR ∞[BkF]=1.7+3/10k.
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Mao, W. Besk-k-Fit bin packing. Computing 50, 265–270 (1993). https://doi.org/10.1007/BF02243816
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DOI: https://doi.org/10.1007/BF02243816