Optimal analysis of Best Fit bin packing

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 b1.7 · OPTc bins. Fur-thermore we show matching lower bounds for all values of Opt, i.e., we give instances on which BestFit uses exactly b1.7 · OPTc bins. Thus we completely settle the worst-case complexity of BestFit bin packing after more than 40 years of its study