Abstract
We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k = 2 and then for the general case of constant k.
Additionally, we present dual approximation schemes for k = 2 and constant k. Thus we show that for any ε> 0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1 + ε.
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Epstein, L., van Stee, R. (2008). Approximation Schemes for Packing Splittable Items with Cardinality Constraints. 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_19
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DOI: https://doi.org/10.1007/978-3-540-77918-6_19
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