Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Voronoi Diagrams

  • Cyrus Shahabi
  • Mehdi Sharifzadeh
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_451

Synonyms

Dirichlet tessellation; Voronoi decomposition; Voronoi tessellation; Thiessen polygons

Definition

The Voronoi diagram of a given set \( P=\left\{{p}_1,\dots, {p}_n\right\} \)
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Recommended Reading

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    Akdogan A, Demiryurek U, Banaei-Kashani F, Shahabi C. Voronoi-based geospatial query processing with MapReduce. CloudCom. Indianapolis/IN/USA: IEEE; 2010, p. 9–16. http://ieeexplore.ieee.org/document/5708428/.
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    de Berg M, van Kreveld M, Overmars M, Schwarzkopf O. Computational geometry: algorithms and applications. 2nd ed. Berlin/Heidelberg/New York: Springer; 2000.zbMATHCrossRefGoogle Scholar
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    Hagedoorn M. Nearest neighbors can be found efficiently if the dimension is small relative to the input size. In: Proceedings of the 9th the International Conference on Database Theory; 2003. p. 440–54.Google Scholar
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    Kolahdouzan M, Shahabi C. Voronoi-based K nearest neighbor search for spatial network databases. In: Proceedings of the 30th the International Conference on Very Large Data Bases; 2004. p. 840–51.CrossRefGoogle Scholar
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    Korn F, Muthukrishnan S. Influence sets based on reverse nearest neighbor queries. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 2000. p. 201–12.CrossRefGoogle Scholar
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    Sharifzadeh M. Spatial query processing using Voronoi diagrams. PhD thesis, Computer Science Department, University of Southern California, Los Angeles. 2007.Google Scholar
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    Sharifzadeh M, Shahabi C. VoR-tree: R-trees with Voronoi diagrams for efficient processing of spatial nearest neighbor queries. Proc. VLDB Endowment. 2010;3(1):1231–42.CrossRefGoogle Scholar
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    Stanoi I, Riedewald M, Agrawal D, El Abbadi A. Discovery of influence sets in frequently updated databases. In: Proceedings of the 27th International Conference on Very Large Data Bases; 2001. p. 99–108.Google Scholar
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    Xu J, Zheng B, Lee W-C, Lee DL. The D-tree: an index structure for planar point queries in location-based wireless services. IEEE Trans Knowl Data Eng. 2004;16(12):1526–42.CrossRefGoogle Scholar
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    Zhang J, Zhu M, Papadias D, Tao Y, Lee DL. Location-based spatial queries. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 2003. p. 443–53.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.GoogleSanta MonicaUSA

Section editors and affiliations

  • Dimitris Papadias
    • 1
  1. 1.Dept. of Computer Science and Eng.Hong Kong Univ. of Science and TechnologyKowloonHong Kong SAR