Adapting the Transformation Technique to Maintain Multi-Dimensional Non-Point Objects in k-d-Tree Based Access Structures

In [10, 18] the transformation technique has been proposed to store k-dimensional intervals { which serve as bounding boxes for arbitrary geometric objects in many applications { as 2k-dimensional points in a point access structure. Unfortunately the transformation technique has two pitfalls: (1) The transformation leads to a skew distribution of the 2k-dimensional image points. (2) Processing a range query searching all objects intersecting a given query region, there is a mismatch between the k-dimensional query region and the 2k-dimensional access structure. In this paper we propose two techniques to overcome these problems which can be directly applied to k-d-tree based point access structures: (1) We present a sophisticated split strategy to determine the split dimension and the split position in case of a bucket split which exploits the knowledge about the distribution of the image points of the transformation technique to gain an extremely exible and robust access structure. (2) We propose a re-transformation of the 2k-dimensional data regions in the access structure into the original k-dimensional data space in order to compare these regions with the k-dimensional query region. Furthermore we state experimental results, which demonstrate, that the presented techniques allow to maintain k-dimensional non-point objects with nearly the same performance as k-dimensional point objects.