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Randomized incremental construction of delaunay and Voronoi diagrams

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Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

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Abstract

In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “online” than earlier similar methods, takes expected time O(n log n) and space O(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.

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Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, USA

    Leonidas J. Guibas & Donald E. Knuth

  2. DEC Systems Research Center, Palo Alto, CA

    Leonidas J. Guibas

  3. Courant Institute of Mathematical Sciences, New York University, USA

    Micha Sharir

  4. School of Mathematical Sciences, Tel Aviv University, Israel

    Micha Sharir

Authors
  1. Leonidas J. Guibas
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  2. Donald E. Knuth
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  3. Micha Sharir
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Editor information

Michael S. Paterson

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© 1990 Springer-Verlag Berlin Heidelberg

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Guibas, L.J., Knuth, D.E., Sharir, M. (1990). Randomized incremental construction of delaunay and Voronoi diagrams. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032048

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  • DOI: https://doi.org/10.1007/BFb0032048

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

  • eBook Packages: Springer Book Archive

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