Analytical Comparison of Two Spatial Data Structures

Region Quadtrees and Bintrees are two structures used in GIS and spatial databases. The expected space performances of these two trees are presented and compared. Analysis is based on the general assumption that the storage requirements of internal and external nodes differ, as well as on a parametric model of binarv random images. Initiallv. formulae that exnress the averaee total storage performance of the two tiees are given: For each” ievel of the Quadtree, formulae-for the average numbers of internal, external white and external black nodes follow. Next, for each level of the Quadtree, the relationship between each node category of the two trees is presented. Based on the formulae developed, we study how the storage requirements of the two trees differ for each Quadtree level. Finally, using the above results, we reach conclusions about the storage efficiency of the most popular implementations and the inverted variations of these two trees (structures that index pictorial databases).