Low Discrepancy Allocation of Two-Dimensional Data

Abstract

Fast browsing and retrieval of geographically referenced information requires the allocation of data on different storage devices for concurrent retrieval. By dividing the two-dimensional space into tiles, a system can allow users to specify regions of interest using a query rectangle and then retrieving information related to tiles covered by the query. Suppose that there are m I/O devices. A tile is labeled by i if the data corresponding to this area is stored in the ith I/O device. A labeling is effcient if the difference of the numbers of occurrences of distinct labels in any given rectangle is small. Except for some simple cases this discrepancy exceeds 1. In the present paper constructions are given to make this discrepancy small relative to m. The constructions use latin squares and a lower bound is given, which shows that the constructions are best possible under certain conditions.

The work of the second and third authors was partially supported by the Hungarian National Foundation for Scientific Research grant number T016389, and European Communities (Cooperation in Science and Technology with Central and Eastern European Countries) contract number CIPACT930113

This research was done while the third author visited The University of British Columbia on a grant of the first author.