Black and White Bin Packing

We introduce the following version of bin packing. The items are of two types (black and white), and in each bin the item types must alternate. We mostly investigate the online scenario. We study the competitiveness of some classical algorithms (First/Best/Worst/Next Fit, Harmonic) — they do not perform very well — and for all online algorithms we also prove the universal lower bound \(1+\frac{1}{2\ln2}\approx1.7213\) which significantly exceeds the known upper bound 1.58889 on classical online bin packing. We also design an online algorithm which is 3-competitive in the absolute sense. A 2.5-approximation algorithm and an APTAS is also given for the offline version.

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