Abstract
On-line algorithms have been extensively studied for the one-dimensional bin packing problem. In this paper we investigate two classes of the one- dimensional bin packing algorithms, and we give lower bounds for their asymptotic worst-case behaviour. For on-line algorithms so far the best lower bound was given by van Vliet in 1992 [13]. 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 \(\frac{248}{161}= 1.54037\ldots\) and we investigate the parametric case as well. For those lists where the elements are preprocessed according to their sizes in decreasing order Csirik et al. [1] proved that no on-line algorithm can have an asymptotic performance ratio smaller than \(\frac{8}{7}\). We improve this result to \(\frac{54}{47}.\)
This research was supported by HSC-DAAD Hungarian-German Research Exchange Program (project P-MÖB/837).
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Balogh, J., Békési, J., Galambos, G. (2011). New Lower Bounds for Certain Classes of Bin Packing Algorithms. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_3
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DOI: https://doi.org/10.1007/978-3-642-18318-8_3
Publisher Name: Springer, Berlin, Heidelberg
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