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Constrained Generalized Delaunay Graphs are Plane Spanners

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Computational Intelligence in Information Systems (CIIS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 532))

Abstract

We look at generalized Delaunay graphs in the constrained setting by introducing line segments which the edges of the graph are not allowed to cross. Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner of the visibility graph.

Research supported in part by FQRNT, NSERC, and Carleton University’s President’s 2010 Doctoral Fellowship.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, Canada

    Prosenjit Bose

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada

    Jean-Lou De Carufel

  3. National Institute of Informatics, Tokyo, Japan

    André van Renssen

  4. JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

    André van Renssen

Authors
  1. Prosenjit Bose
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  2. Jean-Lou De Carufel
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  3. André van Renssen
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Corresponding author

Correspondence to André van Renssen .

Editor information

Editors and Affiliations

  1. School of Computing & Informatics, Universiti Teknologi Brunei School of Computing & Informatics, Gadong, Brunei Darussalam

    Somnuk Phon-Amnuaisuk

  2. School of Computing & Informatics, Universiti Teknologi Brunei School of Computing & Informatics, Gadong, Brunei Darussalam

    Thien-Wan Au

  3. School of Computing & Informatics, Universiti Teknologi Brunei School of Computing & Informatics, Gadong, Brunei Darussalam

    Saiful Omar

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Bose, P., De Carufel, JL., van Renssen, A. (2017). Constrained Generalized Delaunay Graphs are Plane Spanners. In: Phon-Amnuaisuk, S., Au, TW., Omar, S. (eds) Computational Intelligence in Information Systems. CIIS 2016. Advances in Intelligent Systems and Computing, vol 532. Springer, Cham. https://doi.org/10.1007/978-3-319-48517-1_25

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  • DOI: https://doi.org/10.1007/978-3-319-48517-1_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48516-4

  • Online ISBN: 978-3-319-48517-1

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