Abstract
The variable-sized bin packing problem (VBP) is a well-known generalization of the NP-hard bin packing problem (BP) where the items can be packed in bins of M given sizes. The objective is to minimize the total capacity of the bins used. We present an AFPTAS for VBP and BP with performance guarantee \(P(I) \leq (1+ \varepsilon )OPT(I) + O(\log^2(\frac{1}{\varepsilon }))\). The additive term is much smaller than the additive term of already known AFPTAS. The running time of the algorithm is \(O( \frac{1}{\varepsilon ^6} \log\left(\frac{1}{\varepsilon }\right) + \log\left(\frac{1}{\varepsilon }\right) n)\) for bin packing and \(O(\frac{1}{\varepsilon ^{7}} \log^2\left(\frac{1}{\varepsilon }\right) + \log\left(\frac{1}{\varepsilon }\right)\left(M+n\right))\) for variable-sized bin packing, which is an improvement to previously known algorithms.
Keywords
Research supported by DFG project JA612/14-1, “Entwicklung und Analyse von effizienten polynomiellen Approximationsschemata für Scheduling- und verwandte Optimierungsprobleme”.
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Jansen, K., Kraft, S. (2012). An Improved Approximation Scheme for Variable-Sized Bin Packing. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_47
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