Blocking Delaunay Triangulations from Exterior

Oswin Aichholzer, Thomas Hackl, Maarten Löffler, Alexander Pilz, Irene Parada, Manfred Scheucher, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


Given two distinct point sets P and Q in the plane, we say that Q blocks P if no two points of P are adjacent in any Delaunay triangulation of P ∪ Q. Aichholzer et al. (2013) showed that (the Delaunay triangulation of) any set P of n points in general position (that is, no three collinear and no four cocircular) can be blocked by 3
2 n points and that every set P of n points in convex position can be blocked by 5
4 n points. Moreover, they conjectured that, if P is in convex position, n blocking
points are sufficient and necessary. The necessity was recently shown by Biniaz (2021) who proved that every point set in general position requires n blocking points.
Here we investigate the variant, where blocking points can only lie outside of the convex hull of the given point set. We show that 5 4 n − O(1) such exterior-blocking points are sometimes necessary, even if the given point set is in convex position. As a consequence we obtain that, if the conjecture of Aichholzer et al. for the original setting was true, then minimal blocking sets of some point
configurations P would have to contain points inside of the convex hull of P .
Original languageEnglish
Title of host publicationProc. 38th European Workshop on Computational Geometry (EuroCG 2022)
Place of PublicationPerugia, Italy
Publication statusPublished - 2022
Event38th European Workshop on Computational Geometry: EuroCG 2022 - Engineering Department of the University of Perugia, Perugia, Italy
Duration: 14 Mar 202216 Mar 2022


Conference38th European Workshop on Computational Geometry
Abbreviated titleEuroCG 2022
Internet address

Fields of Expertise

  • Information, Communication & Computing


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