Tight degree bounds for pseudo-triangulations of points

Authors:
Lutz Kettner;David Kirkpatrick;Andrea Mantler;Jack Snoeyink;Bettina Speckmann;Fumihiko Takeuchi
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Department of Computer Science, University of British Columbia, Canada;Department of Computer Science, UNC Chapel Hill;Department of Computer Science, UNC Chapel Hill;Institute for Theoretical Computer Science, ETH Zürich, Zürich, Switzerland;Department of Information Science, University of Tokyo, Tokyo, Japan
Venue:
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Year:
2003

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Abstract

We show that every set of n points in general position has a minimum pseudo-triangulation whose maximum vertex degree is five. In addition, we demonstrate that every point set in general position has a minimum pseudotriangulation whose maximum face degree is four (i.e., each interior face of this pseudo-triangulation has at most four vertices). Both degree bounds are tight. Minimum pseudo-triangulations realizing these bounds (individually but not jointly) can be constructed in O(n logn) time.