XZ-Ordering: A Space-Filling Curve for Objects with Spatial Extension

Abstract

There is an increasing need to integrate spatial index structures into commercial database management systems. In geographic information systems (GIS), huge amounts of information involving both, spatial and thematic attributes, have to be managed. Whereas relational databases are adequate for handling thematic attributes, they fail to manage spatial information efficiently. In this paper, we point out that neither a hybrid solution using relational databases and a separate spatial index nor the approach of existing object-relational database systems provide a satisfying solution to this problem. Therefore, it is necessary to map the spatial information into the relational model. Promising approaches to this mapping are based on space-filling curves such as Z-ordering or the Hilbert curve. These approaches perform an embedding of the multidimensional space into the one-dimensional space. Unfortunately, the techniques are very sensitive to the suitable choice of an underlying resolution parameter if objects with a spatial extension such as rectangles or polygons are stored. The performance usually deteriorates drastically if the resolution is chosen too high or too low. Therefore, we present a new kind of ordering which allows an arbitrary high resolution without performance degeneration. This robustness is achieved by avoiding object duplication, allowing overlapping Z-elements, by a novel coding scheme for the Zelements and an optimized algorithm for query processing. The superiority of our technique is shown both, theoretically as well as practically with a comprehensive experimental evaluation.