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An O(N4) algorithm to construct all Voronoi diagrams for k nearest neighbor searching

  • Frank Dehne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)

Abstract

This paper presents an algorithm, that constructs all Voronoi diagrams for k nearest neighbor searching in the Euclidean plane simultaneously. Its space and time complexity of O(N4) is shown to be optimal.

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References

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    Kirkpatrick: Optimal Search in Planar Subdivisions, Department of Computer Science, Univ. of British Columbia, Vancouver, B.C., Canada, Report 81-13, 1981Google Scholar
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    Lee: An Approach to Finding the K-Nearest Neighbor in the Euclidean Plane, Department of Electrical Engineering and Computer Science, Northwestern Univ., Evanston, II. 60201, USA, Report 1981Google Scholar
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    Maurer: The Post-Office Problem and Related Questions, in Noltemeier (ed.): Graphtheoretic Concepts in Computer Science, Proceedings of the International Workshop WG80, Bad Honnef, June 1980, Lecture Notes in Computer Science 100, Springer 1981Google Scholar
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    Shamos: Computational Geometry, Yale University, New Haven, Connecticut,USA, Ph.D.Thesis, 1975Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Frank Dehne
    • 1
  1. 1.Lehrstuhl für Informatik IBayerische Julius-Maximilians-Universität WürzburgWürzburgW.-Germany

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