5 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
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 Od(log d−1 M) independent of the data size, where d is the dimension, M the number of storage devices and d − 1 does not exceed the smallest prime power in the canonical decomposition of M into prime powers. In particular, our schemes work for arbitrary M in dimensions two and three. For general d, they work for all M ≥ d − 1 that are powers of two. Concerning lower bounds, we show that a recent proof of a Ωd(log d−1 2 M) bound contains an error. We close the gap in the proof and thus establish the bound. ∗supported by the DFG-Graduiertenkolleg 357 “Effiziente Algorithmen un
Improved Bounds and Schemes for the Declustering Problem ⋆
Abstract. 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 among the devices. Using deep results from discrepancy theory, we improve previous work of several authors concerning rectangular queries of higher-dimensional data. For this problem, we give a declustering scheme with an additive error of Od(log d−1 M) independent of the data size, where d is the dimension, M the number of storage devices and d−1 not larger than the smallest prime power in the canonical decomposition of M. Thus, in particular, our schemes work for arbitrary M in two and three dimensions, and arbitrary M ≥ d−1 that is a power of two. These cases seem to be the most relevant in applications. For a lower bound, we show that a recent proof of a Ωd(log d−1 2 M) bound contains a critical error. Using an alternative approach, we establish this bound.