Skip to main content
SpringerLink
Log in

Randomized incremental construction of simple abstract Voronoi diagrams in 3-space

Extended abstract

  • Communications
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 965))

Included in the following conference series:

Abstract

The simple abstract Voronoi diagram in 3-space is introduced as an abstraction of the usual Euclidean Voronoi diagram. We show that the three-dimensional simple abstract Voronoi diagram of n sites can be computed in O(n 2 ) expected time using O(n 2 ) expected space by a randomized algorithm.

This work was partly supported by Deutsche Forschungsgemeinschaft grant Kl 655–2.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Aurenhammer: Power diagrams: properties, algorithms and applications. SIAM Journal of Computing 16 (1987), pp. 78–96.

    Google Scholar 

  2. F. Aurenhammer: Voronoi Diagrams — A Survey of a Fundamental Geometric Data Structure. ACM Computer Surveys 23(3), 1991.

    Google Scholar 

  3. J. D. Boissonnat, O. Devillers, R. Schott, M. Teillaud, and M. Yvinec: Applications of random sampling to on-line algorithms in computational geometry. Discrete & Comput. Geom. 8, pp. 51–71, 1992.

    Google Scholar 

  4. K. L. Clarkson and P. W. Shor: Applications of Random Sampling in Computational Geometry, II. Discrete & Comput. Geom. 4, pp. 387–421, 1989.

    Google Scholar 

  5. C. Icking, R. Klein, N.-M. Lê, L. Ma: Convex Distance Functions in 3-Space are Different. Proceedings 9th ACM Symposium on Computational Geometry, 1993.

    Google Scholar 

  6. R. Klein: Concrete and Abstract Voronoi Diagrams. LNCS 400, Springer, 1989.

    Google Scholar 

  7. R. Klein, K. Mehlhorn, and S. Meiser: Randomized Incremental Construction of Abstract Voronoi Diagrams. Comput. Geometry: Theory and Applications 3 (1993), pp. 157–184.

    Google Scholar 

  8. N.-M. Lê: On Voronoi diagrams in the L p -metric in higher dimensions. Proc. 11th STACS, P. Enjalbert et al. (Eds.), LNCS 775, Springer, pp. 711–722, 1994.

    Google Scholar 

  9. N.-M. Lê: An axiomatic approach to Voronoi diagrams in 3-space. Manuscript, 1994.

    Google Scholar 

  10. N.-M. Lê: Randomized incremental construction of simple abstract Voronoi diagrams in 3-space. TR 174, Dep. of Comp. Science, FernUniv. Hagen, Germany.

    Google Scholar 

  11. K. Mehlhorn, S. Meiser, and C. Ó'Dúnlaing: On the Construction of Abstract Voronoi Diagrams. Discrete & Comput. Geom. 6, pp. 211–224, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Praktische Informatik VI, FernUniversität Hagen, D-58084, Hagen, Germany

    Ngoc-Minh Lê

Authors
  1. Ngoc-Minh Lê
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Horst Reichel

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lê, NM. (1995). Randomized incremental construction of simple abstract Voronoi diagrams in 3-space. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_65

Download citation

  • DOI: https://doi.org/10.1007/3-540-60249-6_65

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60249-1

  • Online ISBN: 978-3-540-44770-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation