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(logd-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 d(log d-1 2 M) bound contains a critical error. Using an alternative approach, we establish this bound.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Benjamin Doerr, Nils Hebbinghaus, Sören Werth
• Keywords: CORR 2006, Discrepancy Theory, Education, Storage Devices, Typical Requests