Improved bounds and schemes for the declustering problem

  • Authors:
  • Benjamin Doerr;Nils Hebbinghaus;Sören Werth

  • Affiliations:
  • Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Institut für Informatik, Christian-Albrechts-Universitätzu Kiel, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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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 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 (logd-1M) 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)/2M) bound contains an error. We close the gap in the proof and thus establish the bound.