Binary Quadtree Research Articles

A hierarchical binary quadtree index for spatial queries

An index structure adequate for broadcasting environments must consider the order of data delivery, index size, and selective tuning. This paper introduces a light-weight bit sequence grid-based spatial index, referred to as a binary quadtree, which allows for the sequential search and selective tuning of data. Then, the paper suggests a search algorithm that can efficiently search spatial objects. The results from theoretical analysis and experiments show that the proposed algorithm with the binary quadtree is fast and energy efficient in both range queries and k-nearest neighbor queries.

Compressing quadtrees via common subtree merging

This paper demonstrates that merging common subtrees in binary quadtrees results in significant compression savings. Empirical results on maps from a cartographic database are provided, and theoretical bounds on the amount of compression for certain classes of images are derived.

Multi-colored quadtrees for GIS: Exploiting bit-parallelism for rapid boolean overlay

A number of tesselation based GIS using quadtrees as the underlying data structure have been constructed in recent years. At present there is an almost universal trend towards the representation of a thematic layer as a collection of binary, linear quadtrees, one for each color (value) in the layer. In such a scheme set operations are carried out by taking unions and intersections of binary quadtrees. This paper presents an alternative database scheme where a layer is stored as a single multicolored quadtree, using a bit-list to store values at higher nodes in the tree. This allows the union of any set of values within a layer to be carried out by a single top down traversal of the tree, using parallel bit-masking operations. Experimental evidence is presented to show that these Bit-Mapped Multi-Colored quadtrees lead to faster colour selection and boolean overlay between layers in a GIS. Furthermore, the recent development of One-To-Four and Autumnal quadtrees have meant that it is now possible to exploit the hierarchical structure of regular quadtrees in GIS without paying an associated storage penalty. Experimental results using these developments are presented to show that representing a layer using a Bit-Mapped Multi-Colored quadtree is more space and time efficient for set operations in comparison to the use of a collection of binary quadtrees, one for each value in the layer.

Average efficiency of data structures for binary image processing

This letter adresses the problem of computing the average values associated to geometric decompositions of binary quadtrees, under a faisly general branching process probabilistic model adapted to these types of trees.