Improved Bounds and Schemes for the Declustering Problem

Doerr, Benjamin; Hebbinghaus, Nils; Werth, Sören

Improved Bounds and Schemes for the Declustering Problem

Authors

Doerr, Benjamin

Hebbinghaus, Nils

Werth, Sören

Description

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 $O_d(\log^{d-1} M)$ 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 $M\geq d-1$ that are powers of two. Concerning lower bounds, we show that a recent proof of a $Ω_d(\log^{\frac{d-1}{2}} M)$ bound contains an error. We close the gap in the proof and thus establish the bound.
19 pages, 1 figure