Elsevier

Computational Geometry

Volume 46, Issue 2, February 2013, Pages 154-159
Computational Geometry

Blocking Delaunay triangulations

https://doi.org/10.1016/j.comgeo.2012.02.005Get rights and content
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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 BW 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 n1 white points are always necessary to block a set of n black points.

Keywords

Proximity graphs
Delaunay graph
Graph drawing
Witness graphs

Cited by (0)

1

Partially supported by the Austrian Science Fund (FWF): NFN ‘Industrial Geometry’ S9205-N12 and the ESF EUROCORES programme EuroGIGA – ComPoSe, Austrian Science Fund (FWF): I 648-N18.

2

Partially supported by Conacyt of Mexico, grant 153984.

3

Funded by the Austrian Science Fund (FWF): P23629-N18.

4

Recipient of a DOC-fellowship of the Austrian Academy of Sciences at the Institute for Software Technology, Graz University of Technology, Austria.

5

Partially supported by MEC grants MTM2009-07242, MTM2011-22792 and by the ESF EUROCORES programme EuroGIGA – ComPoSe, grant EUI-EURC-2011-4306. The work was done while the author was visiting the University of Technology, Graz, supported by MICINN Programa Nacional de Movilidad de Recursos Humanos, Plan Nacional de I+D+i 2008–2011.