New lower bounds for certain classes of bin packing algorithms

AbstractOn-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) [12]. 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) [1] proved that no on-line algorithm can have an asymptotic performance ratio smaller than 87. We improve this result to 5447