Using Unbalanced Trees for Indexing Multidimensional Objects

Abstract

In this paper we introduce a new multidimensional index structure called the S-tree. Such indexes are appropriate for a large variety of pictorial databases such as cartography, satellite and medical images. The S-tree discussed in this paper is similar in flavor to the standard R-tree, but accepts mild imbalance in the resulting tree in return for a significantly reduced area, overlap and perimeter in the resulting minimum bounding rectangles. In fact, the S-tree is defined in terms of a parameter which governs the degree to which this trade-off is allowed. We develop an efficient packing algorithm based on this parameter. We then analyze the S-tree analytically, giving theoretical bounds on the degree of imbalance of the tree. We also analyze the S-tree experimentally. The S-tree does well in two dimensions, and even better in three dimensions. Indeed, the S-tree can be expected to do better still as the dimensionality increases. While the S-tree is extremely effective for static databases, we outline the extension to dynamic databases as well.