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On Multiplicatively Weighted Voronoi Diagrams for Lines in the Plane

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Transactions on Computational Science XIII

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 6750))

Abstract

We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n 2 logn) time and O(n 2) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal Θ(n 2) time and space.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Mechanics, Saint Petersburg State University, 28 Universitetsky pr., Stary Peterhof, St Petersburg, 198504, Russia

    Kira Vyatkina

  2. Center for Graphics and Geometric Computing, Dept. of Computer Science, The Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Gill Barequet

  3. Dept. of Computer Science, Tufts University, 161 College Ave., Medford, MA, 02155, USA

    Gill Barequet

Authors
  1. Kira Vyatkina
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  2. Gill Barequet
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Exascala Ltd., Unit 9, 97 Rickman Drive, B15 2AL, Birmingham, UK

    C. J. Kenneth Tan

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Vyatkina, K., Barequet, G. (2011). On Multiplicatively Weighted Voronoi Diagrams for Lines in the Plane. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science XIII. Lecture Notes in Computer Science, vol 6750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22619-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-22619-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22618-2

  • Online ISBN: 978-3-642-22619-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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