Abstract
We study minimum weighted sum bin packing (MWSBP), which is a bin packing problem where the cost of an item is the index of the bin into which it is packed multiplied by its weight, and the goal is to minimize the total cost of the items. This is equivalent to a batch scheduling problem which we define, where the total weighted completion time is to be minimized. This problem is previously known to be NP-hard in the strong sense even for unit weight items. We design a polynomial time approximation scheme for it, and additionally, a dual polynomial time approximation scheme.
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Epstein, L., Levin, A. (2008). Minimum Weighted Sum Bin Packing. In: Kaklamanis, C., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol 4927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77918-6_18
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DOI: https://doi.org/10.1007/978-3-540-77918-6_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77917-9
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