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The θ5-Graph is a Spanner

  • Prosenjit Bose
  • Pat Morin
  • André van Renssen
  • Sander Verdonschot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8165)

Abstract

Given a set of points in the plane, we show that the θ-graph with 5 cones is a geometric spanner with spanning ratio at most \(\sqrt{50 + 22\sqrt{5}}\) ≈ 9.960 . This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses a constructive argument, giving a, possibly self-intersecting, path between any two vertices, whose length is at most \(\sqrt{50 + 22 \sqrt{5}}\) times the Euclidean distance between the vertices. We also give a lower bound on the spanning ratio of \(1\over2\) (11\(\sqrt{5}\)-17) ≈ 3.798.

Keywords

Short Path Inductive Hypothesis Direct Edge Left Corner Total Path Length 
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-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Pat Morin
    • 1
  • André van Renssen
    • 1
  • Sander Verdonschot
    • 1
  1. 1.School of Computer ScienceCarleton UniversityCanada

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