32,216 research outputs found
Lower bounds for several online variants of bin packing
We consider several previously studied online variants of bin packing and
prove new and improved lower bounds on the asymptotic competitive ratios for
them. For that, we use a method of fully adaptive constructions. In particular,
we improve the lower bound for the asymptotic competitive ratio of online
square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201
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
Shapes for maximal coverage for two-dimensional random sequential adsorption
The random sequential adsorption of various particle shapes is studied in
order to determine the influence of particle anisotropy on the saturated random
packing. For all tested particles there is an optimal level of anisotropy which
maximizes the saturated packing fraction. It is found that a concave shape
derived from a dimer of disks gives a packing fraction of 0.5833, which is
comparable to the maximum packing fraction of ellipsoids and spherocylinders
and higher than any other studied shape. Discussion why this shape is so
beneficial for random sequential adsorption is given.Comment: 6 pages, 8 figures, 3 table
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