Tight results for Next Fit and Worst Fit with resource augmentation

It is well known that the two simple algorithms for the classic bin packing problem, and both have an approximation ratio of 2. However, seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used.Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b>1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of and of , and use it to show that is strictly better than for any 1