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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Optimal Analysis of Best Fit Bin Packing
verfasst von : György Dósa, Jiří Sgall
Erschienen in: Automata, Languages, and Programming
Verlag: Springer Berlin Heidelberg
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In early seventies it was shown that the
asymptotic
approximation ratio of
BestFit
bin packing is equal to 1.7. We prove that also the
absolute
approximation ratio for
BestFit
bin packing is exactly 1.7, improving the previous bound of 1.75. This means that if the optimum needs
Opt
bins,
BestFit
always uses at most
$\lfloor1.7\cdot$
OPT
$\rfloor$
bins. Furthermore we show
matching lower bounds
for all values of
Opt
, i.e., we give instances on which
BestFit
uses exactly
$\lfloor1.7\cdot$
OPT
$\rfloor$
bins. Thus we completely settle the worst-case complexity of
BestFit
bin packing after more than 40 years of its study.