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On the construction of abstract voronoi diagrams

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STACS 90 (STACS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 415))

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Abstract

We show that the abstract Voronoi diagram of n sites in the plane can be constructed in time O(n log n) by a randomized algorithm. This yields an alternative, but simpler, O(n log n) algorithm in many previously considered cases and the first O(n log n) algorithm in some cases, e.g., disjoint convex sites with the Euclidean distance function. Abstract Voronoi diagrams are given by a family of bisecting curves and were recently introduced by Klein [Kl88a]. Our algorithm is based on Clarkson and Shor's randomized incremental construction technique [CS].

This work was supported by the DFG, Me 620/6, and ESPRIT P3075 ALCOM

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Authors and Affiliations

  1. FB Informatik Universität des Saarlandes, D-6600, Saarbrücken, West Germany

    K. Mehlhorn & St. Meiser

  2. Department of Mathematics, Trinity College Dublin, Dublin, Ireland

    C. Ó'Dúnlaing

Authors
  1. K. Mehlhorn
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  2. St. Meiser
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  3. C. Ó'Dúnlaing
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Christian Choffrut Thomas Lengauer

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© 1990 Springer-Verlag Berlin Heidelberg

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Mehlhorn, K., Meiser, S., Ó'Dúnlaing, C. (1990). On the construction of abstract voronoi diagrams. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_46

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  • DOI: https://doi.org/10.1007/3-540-52282-4_46

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  • Print ISBN: 978-3-540-52282-9

  • Online ISBN: 978-3-540-46945-2

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