Blocking Delaunay triangulations

Authors:
Oswin Aichholzer;Ruy Fabila-Monroy;Thomas Hackl;Marc Van Kreveld;Alexander Pilz;Pedro Ramos;Birgit Vogtenhuber
Affiliations:
Institute for Software Technology, University of Technology, Graz, Austria;Departamento de Matemáticas, Cinvestav, México, Mexico;Institute for Software Technology, University of Technology, Graz, Austria;Department of Computer Science, Utrecht University, Utrecht, The Netherlands;Institute for Software Technology, University of Technology, Graz, Austria;Departamento de Matemáticas, Universidad de Alcalá, Madrid, Spain;Institute for Software Technology, University of Technology, Graz, Austria
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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Abstract

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of B@?W there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) 3n/2 white points are always sufficient to block a set of n black points, (ii) if B is in convex position, 5n/4 white points are always sufficient to block it, and (iii) at least n-1 white points are always necessary to block a set of n black points.