A Two-Phase Algorithm for Bin Stretching with Stretching Factor 1.5

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of $1.5$ for any number of bins. We build on previous algorithms and use a two-phase approach. We also show that this approach cannot give better results by proving a matching lower bound.