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Nearest Neighbour Graph and Locally Minimal Triangulation

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10405))

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Abstract

Nearest neighbour graph (NNG) is a useful tool namely for collision detection tests. It is well known that NNG, when considered as an undirected graph, is a subgraph of Delaunay triangulation (DT) and this relation can be used for efficient NNG computation. This paper concentrates on relation of NNG to the locally minimal triangulation (LMT) and shows that, although NNG can be proved not to be a LMT subgraph, in most cases LMT contains all or nearly all NNG edges. This fact can also be used for NNG computation, namely in kinetic problems, because LMT computation is easier.

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Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic, the project SGS-2016-013 Advanced Graphical and Computing Systems and the project PUNTIS (LO1506) under the program NPU I. 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

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

    Andrej Ferko

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

    Ivana Kolingerová & Martin Maňák

Authors
  1. Ivana Kolingerová
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  2. Andrej Ferko
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  3. Tomáš Vomáčka
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  4. Martin Maňák
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Corresponding author

Correspondence to Ivana Kolingerová .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Kolingerová, I., Ferko, A., Vomáčka, T., Maňák, M. (2017). Nearest Neighbour Graph and Locally Minimal Triangulation. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10405. Springer, Cham. https://doi.org/10.1007/978-3-319-62395-5_31

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  • DOI: https://doi.org/10.1007/978-3-319-62395-5_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62394-8

  • Online ISBN: 978-3-319-62395-5

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