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Computer Science, Data Structures and Algorithms, cs.DS
Abstract:
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.
