I want to compare the R-Tree and the Quadtree for geospatial data. While there is literature out there I struggle to find documents that cover real basic comparison. So I decided to ask this question.
In my opinion, the R-Tree has the advantage of being balanced and the tree has no empty leaves. As a disadvantage, the basic operation like insert or delete could result in restructering the whole index.
The Quadtree is the opposite, it is not balanced and has empty leaves, but it does not need to be restrctured.
So as a fazit from that I would say that the R-Tree does need less memory and is faster for searching because of the minimal height. The quadtree is better when there are many update-operations, but the resulting tree could be unbalanced.
Are these points correct in your opinion? Are there any good documents out there that cover this topic?
Auf Wiedersehen, Andre
The difference (algorithmically) is: in quadtrees, the data reaching a node is split into a fixed (2^d), equal size cells, whereas in kdtrees, the data is split into two regions based on some data analysis (e.g. the median of some coordinate).
R-tree is a tree data structure used for storing spatial data indexes in an efficient manner. R-trees are highly useful for spatial data queries and storage. Some of the real life applications are mentioned below: Indexing multi-dimensional information. Handling geospatial coordinates.
A B-Tree allows you to efficiently search orderable items in secondary memory (like a hard disk), and an R-Tree allows you to efficiently search for elements which are "at" or "near" a particular point or bounding box, also in secondary memory.
For polygons: The search time in the quad-kd tree is reduced by 71.4% compared to quad-tree and 55.6% compared to kd-tree. For points and polygons from a GIS map: The search time in the quad-kd tree is reduced by 67.47% compared to kd-tree and 51.3% compared to quad-tree.
Here's paper which has pretty nice comparison of QuadTrees and R Trees:
Quadtree and R-tree Indexes in Oracle Spatial: A Comparison using GIS Data
Some differences:
"restructuring the whole index". No. Restructuring the R-tree is restricted to a single path, not the "whole" index. It works similar to the B-tree, actually.
Consider implementing both, and doing some benchmarks yourself, to really know how they perform. Don't only use theory.
On uniformly distributed data with a high change frequency, quadtrees will usually work better. On disk, the R-tree has clear advantages.
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