Years and Authors of Summarized Original Work
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2002; Hjaltason, Samet
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2006; Agarwal, Arge, Danner
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2010; de Berg, Haverkort, Thite, Toma
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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 [10]. While their worst-case behavior is good only in some simple cases, quadtrees...
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Recommended Reading
Agarwal PK, Arge L, Danner A (2006) From point cloud to grid DEM: a scalable approach. In: Proceedings of the 12th symposium on spatial data handling, Vienna, pp 771–788
de Berg M, Haverkort H, Thite S, Toma L (2010) Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions. Comput Geom 43(5):493–513
Gargantini I (1982) An effective way to represent quadtrees. Commun ACM 25(12):905–910
Haverkort H, Toma L, Wei BP (2013) An edge quadtree for external memory. In: Proceedings of the 12th international symposium on experimental algorithms, Rome, pp 115–126
Hjaltason G, Samet H (1999) Improved bulk-loading algorithms for quadtrees. In: Proceedings of the ACM international symposium on advances in GIS, Kansas City, pp 110–115
Hjaltason GR, Samet H (2002) Speeding up construction of PMR quadtree-based spatial indexes. VLDB J 11:190–137
Hjaltason G, Samet H, Sussmann Y (1997) Speeding up bulk-loading of quadtrees. In: Proceedings of the ACM international symposium on advances in GIS, Las Vegas
Löffler M, Mulzer W (2011) Triangulating the square and squaring the triangle: quadtrees and delaunay triangulations are equivalent. In: Proceedings of the 22nd ACM-SIAM symposium on discrete algorithms (SODA), San Francisco, pp 1759–1777
Nelson R, Samet H (1987) A population analysis for hierarchical data structures. In: Proceeding of the SIGMOD, San Francisco, pp 270–277
Samet H (2006) Foundations of multidimensional and metric data structures. Morgan-Kaufmann, San Francisco
Samet H, Webber R (1985) Storing a collection of polygons using quadtrees. ACM Trans Graph 4(3):182–222
Samet H, Shaffer C, Webber R (1986) The segment quadtree: a linear quadtree-based representation for linear features. In: Data structures for raster graphics pp 91–123
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Haverkort, H., Toma, L. (2016). Quadtrees and Morton Indexing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_585
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