Amortized efficiency of list update and paging rules
Communications of the ACM
The relative worst order ratio for online algorithms
ACM Transactions on Algorithms (TALG)
On the separation and equivalence of paging strategies
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Paging and list update under bijective analysis
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Comparison of Performance Measures for Online Algorithms
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Fast algorithms for bin packing
Journal of Computer and System Sciences
Tight results for Next Fit and Worst Fit with resource augmentation
Theoretical Computer Science
Tighter bounds of the First Fit algorithm for the bin-packing problem
Discrete Applied Mathematics
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We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items @a. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of @a for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127~1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.