Improved Lower Bounds for Online Hypercube Packing

Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing hypercubes into bins in two or more dimensions, once for general algorithms (in two dimensions) and once for an important subclass, so-called Harmonic-type algorithms (in two or more dimensions). Lastly, we show that two adaptions of the ideas from the best known one-dimensional packing algorithm to square packing also do not help to break the barrier of 2.