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Optimal, Suboptimal, and Robust Algorithms for Proximity Graphs

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Algorithms and Data Structures (WADS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

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Abstract

Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γtO,γ1] values that result in non-planar graphs. For β = 1, we show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n 2) time. Research supported in part by the CNR Project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed al CAD”, the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%), by Gen. Cat. SGR000356 and MEC-DGES-SEUID PB98-0933, Spain, and by NSERC, Canada.

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Author information

Authors and Affiliations

  1. Departament de Matemática Aplicada II, Universitat Politécnica de Catalunya, Barcelona, Spain

    Ferran Hurtado

  2. Dipartimento di Ingegneria Elettronica e dellÍnformazione, Universitá di Perugia, Perugia, Italy

    Giuseppe Liotta

  3. Department of Computing and Information Science, Queenś University, Kingston, Ontario, Canada

    Henk Meijer

Authors
  1. Ferran Hurtado
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  2. Giuseppe Liotta
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  3. Henk Meijer
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Candada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. Center for Geometric Computing, Brown University, Providence, RI, 02912-1910, USA

    Roberto Tamassia

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© 2001 Springer-Verlag Berlin Heidelberg

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Hurtado, F., Liotta, G., Meijer, H. (2001). Optimal, Suboptimal, and Robust Algorithms for Proximity Graphs. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_2

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  • DOI: https://doi.org/10.1007/3-540-44634-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

  • eBook Packages: Springer Book Archive

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