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On Plane Constrained Bounded-Degree Spanners

  • Prosenjit Bose
  • Rolf Fagerberg
  • André van Renssen
  • Sander Verdonschot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)

Abstract

Let P be a set of points in the plane and S a set of non-crossing line segments with endpoints in P. The visibility graph of P with respect to S, denoted \(\mathord{\it Vis}(P,S)\), has vertex set P and an edge for each pair of vertices u,v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ 6-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of \(\mathord{\it Vis}(P,S)\). We then show how to construct a plane 6-spanner of \(\mathord{\it Vis}(P,S)\) with maximum degree 6 + c, where c is the maximum number of segments adjacent to a vertex.

Keywords

Induction Hypothesis Positive Cone Visibility Graph Negative Cone Canonical Sequence 
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 2012

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Rolf Fagerberg
    • 2
  • André van Renssen
    • 1
  • Sander Verdonschot
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Dept. of Mathematics and Computer ScienceUniversity of Southern DenmarkDenmark

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