9,244 research outputs found
Improved Bounds and Schemes for the Declustering Problem
The declustering problem is to allocate given data on parallel working
storage devices in such a manner that typical requests find their data evenly
distributed on the devices. Using deep results from discrepancy theory, we
improve previous work of several authors concerning range queries to
higher-dimensional data. We give a declustering scheme with an additive error
of independent of the data size, where is the
dimension, the number of storage devices and does not exceed the
smallest prime power in the canonical decomposition of into prime powers.
In particular, our schemes work for arbitrary in dimensions two and three.
For general , they work for all that are powers of two.
Concerning lower bounds, we show that a recent proof of a
bound contains an error. We close the gap in
the proof and thus establish the bound.Comment: 19 pages, 1 figur
Two floor building needing eight colors
Motivated by frequency assignment in office blocks, we study the chromatic
number of the adjacency graph of -dimensional parallelepiped arrangements.
In the case each parallelepiped is within one floor, a direct application of
the Four-Colour Theorem yields that the adjacency graph has chromatic number at
most . We provide an example of such an arrangement needing exactly
colours. We also discuss bounds on the chromatic number of the adjacency graph
of general arrangements of -dimensional parallelepipeds according to
geometrical measures of the parallelepipeds (side length, total surface or
volume)
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