Advertisement

Discrete & Computational Geometry

, Volume 4, Issue 5, pp 423–432 | Cite as

A fast las vegas algorithm for triangulating a simple polygon

  • Kenneth L. Clarkson
  • Robert E. Tarjan
  • Christopher J. Van Wyk
Article

Abstract

We present a randomized algorithm that triangulates a simple polygon onn vertices inO(n log*n) expected time. The averaging in the analysis of running time is over the possible choices made by the algorithm; the bound holds for any input polygon.

Keywords

Line Segment Discrete Comput Geom Computational Geometry Recursive Call Vertical Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [ACG]
    M. J. Atallah, R. Cole, and M. T. Goodrich, Cascading divide-and-conquer: a technique for designing parallel algorithms,Proceedings of the 28th Annual Symposium on Foundations of Computer Science, 1987, pp. 151–160.Google Scholar
  2. [CI]
    B. Chazelle and J. Incerpi, Triangulation and shape complexity,ACM Transactions on Graphics,3 (1984), 135–152.zbMATHCrossRefGoogle Scholar
  3. [C1]
    K. L. Clarkson, New applications of random sampling in computational geometry,Discrete and Computational Geometry,2 (1987), 195–222.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [C2]
    K. L. Clarkson, Applications of random sampling in computational geometry, II,Proceedings of the Fourth Annual Symposium on Computational Geometry, 1988, pp. 1–11.Google Scholar
  5. [CCT]
    K. L. Clarkson, R. Cole, and R. E. Tarjan, private communication.Google Scholar
  6. [CS]
    K. L. Clarkson and P. W. Shor, Applications of random sampling in computational geometry, II,Discrete and Computational Geometry, this issue, 387–421.Google Scholar
  7. [CTV]
    K. L. Clarkson, R. E. Tarjan, and C. J. Van Wyk, A fast Las Vegas algorithm for triangulating a simple polygon,Proceedings of the Fourth Annual Symposium on Computational Geometry, 1988, pp. 18–22.Google Scholar
  8. [ES]
    P. Erdos and J. Spencer,Probabilistic Methods in Combinatorics, Academic Press, New York, 1974.Google Scholar
  9. [FM]
    A. Fournier and D. Y. Montuno, Triangulating simple polygons and equivalent problems,ACM Transactions on Graphics,3 (1984), 153–174.zbMATHCrossRefGoogle Scholar
  10. [FNTV]
    K. Y. Fung, T. M. Nicholl, R. E. Tarjan, and C. J. Van Wyk, Simplified linear-time Jordan sorting and polygon clipping,ACM Transactions on Graphics, submitted.Google Scholar
  11. [GJPT]
    M. R. Garey, D. S. Johnson, F. P. Preparata, and R. E. Tarjan, Triangulating a simple polygon,Information Processing Letters,7 (1978), 175–180.zbMATHMathSciNetCrossRefGoogle Scholar
  12. [HW]
    D. Haussler and E. Welzl,ɛ-nets and simplex range queries,Discrete and Computational Geometry,2 (1987), 127–151.zbMATHMathSciNetCrossRefGoogle Scholar
  13. [HMRT]
    K. Hoffman, K. Mehlhorn, P. Rosenstiehl, and R. Tarjan, Sorting Jordan sequences in linear time using level-linked search trees,Information and Control,68 (1986), 170–184.MathSciNetCrossRefGoogle Scholar
  14. [PS]
    F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.CrossRefGoogle Scholar
  15. [TV]
    R. E. Tarjan and C. J. Van Wyk, AnO(n log logn)-time algorithm for triangulating a simple polygon,SIAM Journal on Computing,17 (1988), 143–178.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Kenneth L. Clarkson
    • 1
  • Robert E. Tarjan
    • 1
    • 2
  • Christopher J. Van Wyk
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA

Personalised recommendations