A Study on Grid Partition for Declustering High-Dimensional Data

Abstract

Most of the previous work on declustering have been focused on proposing good mapping functions under the assumption that the data space is partitioned equally for all dimensions. In this paper, we relax equal partition restriction on all dimensions by choosing smaller number of dimensions as split axes and study the effects of grid-like partitioning methods on the performance of a mapping function which is widely used for declustering algorithms. For this, we propose a cost model to expect the number of grid cells intersecting a range query and apply the best mapping scheme so far to the partitioned grid cells. Experiments show that our cost model gives remarkable accuracy for all ranges of selectivities and dimensions. By applying different partitioning schemes on the Kronecker sequence mapping function [5], which is known to be the best mapping function for high-dimensional data so far, we can achieve up to 23 times performance gain. Thus we can conclude that the performance of a mapping function is highly dependent on partitioning schemes applied. And our cost model gives clear criteria on how to select the number of split dimensions out of d dimensions to achieve better performance of a mapping function on declustering.