Constrained Generalized Delaunay Graphs are Plane Spanners

  • Prosenjit Bose
  • Jean-Lou De Carufel
  • André van RenssenEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 532)


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.


Line Segment Isosceles Triangle Visibility Graph Geometric Graph Convex Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Jean-Lou De Carufel
    • 2
  • André van Renssen
    • 3
    • 4
    Email author
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.School of Electrical Engineering and Computer ScienceUniversity of OttawaOttawaCanada
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan

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