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Towards Plane Spanners of Degree 3

Authors Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Cyril Gavoille, Anil Maheshwari, Michiel Smid

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Keywords
  • plane spanners
  • degree-3 spanners
  • convex position
  • non-uniform lattice

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Abstract

Let S be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane frac{3+4 pi}{3}-spanner of S whose vertex degree is at most 3. Let Lambda be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane 3 sqrt{2}-spanner for Lambda whose vertex degree is at most 3. For points that are in the plane and in general position, we show how to compute plane degree-3 spanners with a linear number of Steiner points.

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Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Cyril Gavoille, Anil Maheshwari, and Michiel Smid. Towards Plane Spanners of Degree 3. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ISAAC.2016.19

Author Details

Ahmad Biniaz
Prosenjit Bose
Jean-Lou De Carufel
Cyril Gavoille
Anil Maheshwari
Michiel Smid

References

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