# Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_585

## Years and Authors of Summarized Original Work

• 2002; Hjaltason, Samet

• 2006; Agarwal, Arge, Danner

• 2010; de Berg, Haverkort, Thite, Toma

• 2013; McGranaghan, Haverkort, Toma

## Problem Definition

The quadtree describes a class of data structures for geometric objects. A quadtree partitions space hierarchically using a stopping rule that decides when a region is small enough so that it does not need to be subdivided further. If the space is d dimensional, a quadtree recursively divides a d-dimensional hypercube containing the input data into 2d hypercubes until each region satisfies the given stopping rule. In 2D, the hypercubes are squares. Three-dimensional quadtrees are also known as octrees. Quadtrees have been used for many types of data, such as points, line segments, polygons, rectangles, curves, and images, and for many types of applications. For a detailed presentation, we refer to the book by Samet . While their worst-case behavior is good only in some simple cases, quadtrees...

## Keywords

IO-efficient algorithms Segment intersection Space decomposition Space-filling curve
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