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Transactions on Computational Science XXXIII pp 115–127Cite as

Neighbourhood Graphs and Locally Minimal Triangulations

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Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 10990))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Computer Science, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Ivana Kolingerová, Tomáš Vomáčka & Martin Maňák

  2. New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Ivana Kolingerová & Martin Maňák

  3. Department of Algebra, Geometry and Didactics of Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

    Andrej Ferko

Authors
  1. Ivana Kolingerová
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  2. Tomáš Vomáčka
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  3. Martin Maňák
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  4. Andrej Ferko
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Correspondence to Ivana Kolingerová .

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Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Sardina Systems OÜ, Tallinn, Estonia

    C.J. Kenneth Tan

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Kolingerová, I., Vomáčka, T., Maňák, M., Ferko, A. (2018). Neighbourhood Graphs and Locally Minimal Triangulations. In: Gavrilova, M., Tan, C. (eds) Transactions on Computational Science XXXIII. Lecture Notes in Computer Science(), vol 10990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58039-4_7

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  • DOI: https://doi.org/10.1007/978-3-662-58039-4_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-58038-7

  • Online ISBN: 978-3-662-58039-4

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