On the Stretch Factor of the Theta-4 Graph

  • Luis Barba
  • Prosenjit Bose
  • Jean-Lou De Carufel
  • André van Renssen
  • Sander Verdonschot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

In this paper we show that the θ-graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ-graph for which it was not known whether its stretch factor was bounded.

Keywords

computational geometry geometric spanners θ-graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Luis Barba
    • 1
    • 2
  • Prosenjit Bose
    • 1
  • Jean-Lou De Carufel
    • 1
  • André van Renssen
    • 1
  • Sander Verdonschot
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium

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