It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF 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 WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1. © 2010 Elsevier B.V. All rights reserved.
Boyar, J., Epstein, L., & Levin, A. (2010). Tight results for Next Fit and Worst Fit with resource augmentation. Theoretical Computer Science, 411(26–28), 2572–2580. https://doi.org/10.1016/j.tcs.2010.03.019