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Algorithmica

pp 1–24 | Cite as

On Plane Constrained Bounded-Degree Spanners

  • Prosenjit Bose
  • Rolf Fagerberg
  • André van Renssen
  • Sander Verdonschot
Article
  • 36 Downloads

Abstract

Let P be a finite 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 \(\mathord { Vis}(P,S)\), has vertex set P and an edge for each pair of vertices uv in P for which no line segment of S properly intersects uv. We show that the constrained half-\(\theta _6\)-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of \(\mathord { Vis}(P,S)\). We then show how to construct a plane 6-spanner of \(\mathord { Vis}(P,S)\) with maximum degree \(6+c\), where c is the maximum number of segments of S incident to a vertex.

Keywords

Plane spanners Bounded-degree Constraints Visibility graph 

Notes

Acknowledgements

This work is supported in part by the Natural Science and Engineering Research Council of Canada, Carleton University’s President’s 2010 Doctoral Fellowship, the Ontario Ministry of Research and Innovation, and the Danish Council for Independent Research, Natural Sciences, Grant DFF-1323-00247, and JST ERATO Grant No. JPMJER1201, Japan.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  3. 3.School of Information TechnologiesUniversity of SydneySydneyAustralia

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