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A space efficient algorithm for the greedy triangulation

  • Computational Geometry
  • Conference paper
  • First Online:
System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 113))

Abstract

An algorithm for constructing the greedy triangulation of any planar straight-line graph with n vertices in time O(n 2 log n) and space O(n) is presented. The upper time-space bound implied by the algorithm in particular improves Gilbert's simultaneous O(n 2 log n)-time and O(n 2)-space bound for finding the greedy triangulation of an n-point planar point set. A theorem suggesting a good expected time-performance of the presented algorithm is proven.

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References

  1. Takao Asano and Tetsuo Asano, Voronoi Diagram for Points in a Simple Polygon, manuscript, Sophia University, Tokyo.

    Google Scholar 

  2. S. Fortune, A Sweepline Algorithm for Voronoi Diagrams, in the proceedings of the 2nd ACM Symposium on Computational Geometry, Yorktown Heights, New York.

    Google Scholar 

  3. P.D. Gilbert, New Results in Planar Triangulations, M.S. Thesis, Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.

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  4. A. Lingas, Voronoi Diagrams with Barriers and the Shortest Diagonal Problem, submitted.

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  5. D.T. Lee and A. Lin, Generalized Delaunay Triangulation for Planar Graphs, to appear in Discrete and Computational Geometry, Springer Verlag.

    Google Scholar 

  6. K. Mehlhorn, Data Structures and Algorithms, EATS M.T.C.S, Springer Verlag, N.Y.

    Google Scholar 

  7. G.K. Manacher, and A.L. Zorbrist, The use of probabilistic methods and of heaps for fast-average-case, space-optimal greedy algorithms (extended abstract), manuscript.

    Google Scholar 

  8. J. Niervergelt and F.P. Preparata, Plane-sweeping algorithms for intersecting geometric figures, Commun. ACM., vol. 25, no. 10. pp. 739–747.

    Google Scholar 

  9. T. Ohya, M.Iri, K. Murota, Improvements of the Incremental Method for the Voronoi Diagram with Computational Comparison of Various Algorithms, Journal of the Operations Research Society of Japan, Vol 27(4), pp. 306–336.

    Google Scholar 

  10. F.P. Preparata and M.I. Shamos, Computational Geometry, An Introduction, Texts and Monographs in Computer Science, Springer Verlag, New York.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Andrzej Lingas

Authors
  1. Andrzej Lingas
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Editor information

Masao Iri Keiji Yajima

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© 1988 International Federation for Information Processing

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Lingas, A. (1988). A space efficient algorithm for the greedy triangulation. In: Iri, M., Yajima, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042804

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  • DOI: https://doi.org/10.1007/BFb0042804

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19238-1

  • Online ISBN: 978-3-540-39164-7

  • eBook Packages: Springer Book Archive

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