Optimal Redundancy in Spatial Database Systems

In spatial database systems rectangles are commonly used to approximate real spatial data. A technique that approximates extended objects with a collection of rectangles is the z-ordering method. Since each of these rectangles eventually corresponds to an entry in a spatial index, the object may be refer-enced several times. This redundancy eeect is controllable. In this paper, we present an empirically derived formula to assess the expected redundancy for the z-ordering approximation technique given some simple parameters. After showing the applicability of this formula to a large class of diierent object geometries, we make use of this result to determine the optimal redundancy for real spatial data by means of theoretical considerations. In order to verify our theoretical results, we conducted several experiments using real spatial data and found a good correspondence.