D-tree: a Bi-level Technique for Indexing Rectangle Data in Spatial Database Systems

This paper shows how a domain-decomposition hierarchy can be organized as a paginated tree with a balanced height, which can be further extended to index the data subsets (i.e., rst-level indexing). The data in each subset can be indexed using any existing access support structure. (i.e., second-level indexing). We call this bi-level indexing structure \D-tree". D-tree has many desirable properties including its good data clustering characteristics, its insusceptibil-ity to the insertion order of the data set, and its immunity to the skew in the access patterns and data distributions. We provide experimental results to demonstrate these beneets. They show that D-trees using R-trees as the second-level indices provide savings averaging 90% over using R-tree alone. In general, the proposed technique can be used to boost the performance of any existing spatial indexing methods (e.g., R-tree, R +-tree, etc.) 1 Introduction Spatial data are expensive to retrieve due to the nature of the problem, that is, spatial data cannot be sorted or hashed like one-dimensional data. Numerous indexing techniques have been developed for spatial data in the past decades. Basically, they can be divided into two classes. The rst one deals with spatial data as points in a multidimensional space. This class includes point quadtree, k-d tree, K-D-B tree, hB-tree and so forth. These structures can be clas-siied as point trees. Normally, the shape of point trees is highly dependent on the order in which the data points are inserted. On the other hand, the second class can be called regional tree, in which spatial data are represented by intervals in several dimensions. Such spatial data normally are called regional data. For example, a rectangle is an object identiied by two points in a two dimensional space. This class includes R-tree and its variants. In this paper, we focus on rectangle data. Rectangles are often used to approximate other objects in an image for which they serve as the minimum rectilinear enclosing object. Of course, the exact boundaries of the object are also stored, but they are only accessed if greater precision is needed. The two most important types of operations on such data sets are window operations (i.e., rectangular range query) and spatial join operations. These operations are very expensive to perform. To reduce their execution time, the spatial data must be clustered. Unlike conventional textual databases, clustering in this case must base on the space occupied by the data. …