Neighbourhood Graphs and Locally Minimal Triangulations

  • Ivana KolingerováEmail author
  • Tomáš Vomáčka
  • Martin Maňák
  • Andrej Ferko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10990)


Neighbourhood (or proximity) graphs, such as nearest neighbour graph, closest pairs, relative neighbourhood graph and k-nearest neighbour graph are useful tools in many tasks inspecting mutual relations, similarity and closeness of objects. Some of neighbourhood graphs are subsets of Delaunay triangulation (DT) and this relation can be used for efficient computation of these graphs. This paper concentrates on relation of neighbourhood graphs to the locally minimal triangulation (LMT) and shows that, although generally these graphs are not LMT subgraphs, in most cases LMT contains all or many edges of these graphs. This fact can also be used for the neighbourhood graphs computation, namely in kinetic problems, because LMT computation is easier.


Nearest neighbour graph K-nearest neighbour graph Locally minimal triangulation Delaunay triangulation Kinetic problem 



This work was supported by the Czech Science Foundation, the project number 17-07690S, and by the Ministry of Education, Youth and Sports of the Czech Republic, project number LO1506 (PUNTIS). We would like to thank to T. Bayer from the Charles University in Prague, Czech Republic for supplying us the real terrain data for the experiments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ivana Kolingerová
    • 1
    • 2
    Email author
  • Tomáš Vomáčka
    • 1
  • Martin Maňák
    • 1
    • 2
  • Andrej Ferko
    • 3
  1. 1.Department of Computer Science, Faculty of Applied SciencesUniversity of West BohemiaPilsenCzech Republic
  2. 2.New Technologies for the Information Society, Faculty of Applied SciencesUniversity of West BohemiaPilsenCzech Republic
  3. 3.Department of Algebra, Geometry and Didactics of Mathematics, Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia

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