Blocking delaunay triangulations

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

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Oswin Aichholzer, Ruy Fabila Monroy, Thomas Hackl, Alexander Pilz, Pedro Ramos, Marc J. van Kreveld, Birgit Vogtenhuber
• Keywords: Blue Points, CCCG 2010, Computational Geometry, Delaunay Triangulation, Red Points