On-line algorithms have been extensively studied for the one-dimensional bin packing problem. In this paper, we investigate two classes of one-dimensional bin packing algorithms, and we give better lower bounds for their asymptotic worst-case behavior. For on-line algorithms so far the best lower bound was given by van Vliet in (1992) . He proved that there is no on-line bin packing algorithm with better asymptotic performance ratio than 1.54014.... In this paper, we give an improvement on this bound to 248161=1.54037... and we investigate the parametric case as well. For those lists where the elements are preprocessed according to their sizes in non-increasing order, Csirik et al. (1983)  proved that no on-line algorithm can have an asymptotic performance ratio smaller than 87. We improve this result to 5447. © 2012 Elsevier B.V. All rights reserved.
Balogh, J., Békési, J., & Galambos, G. (2012). New lower bounds for certain classes of bin packing algorithms. Theoretical Computer Science, 440–441, 1–13. https://doi.org/10.1016/j.tcs.2012.04.017