A randomized algorithm for triangulating a simple polygon in linear time

Discrete and Computational Geometry

Volumn 26, Issue 2, 2001, Pages 245-265

  Amato, N M ^a   Goodrich, M T ^b   Ramos, E A ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b Johns Hopkins University   (United States)

^c MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035646614     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-001-0027-x     Document Type: Article

References (21)

1. P. K. Agarwal, M. de Berg, J. Matoušek, and O. Schwarzkopf. Constructing levels in arrangements and higher order Voronoi diagrams. SIAM J. Comput., 27:654-667, 1998.
2. T. Asano, T. Asano, and R. Y. Pinter. Polygon triangulation: efficiency and minimality. J. Algorithms, 7:221-231, 1986.
3. B. Chazelle. Triangulating a simple polygon in linear time. Discrete Comput. Geom., 6(5):485-524, 1991.
4. B. Chazelle and J. Friedman. A deterministic view of random sampling and its use in geometry. Combinatorica, 10(3):229-249, 1990.
5. B. Chazelle and J. Incerpi. Triangulation and shape-complexity. ACM Trans. Graph., 3(2):135-152, 1984.
6. K. L. Clarkson, R. Cole, and R. E. Tarjan. Erratum: Randomized parallel algorithms for trapezoidal diagrams. Internat. J. Comput. Geom. Appl., 2(3):341-343, 1992.
7. K. L. Clarkson, R. Cole, and R. E. Tarjan. Randomized parallel algorithms for trapezoidal diagrams. Internat. J. Comput. Geom. Appl., 2(2):117-133, 1992.
8. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
9. K. L. Clarkson, R. E. Tarjan, and C. J. Van Wyk. A fast Las Vegas algorithm for triangulating a simple polygon. Discrete Comput. Geom., 4:423-432, 1989.
10. M. de Berg, K. Dobrindt, and O. Schwarzkopf. On lazy randomized incremental construction. Discrete Comput. Geom., 14:261-286, 1995.
11. A. Fournier and D. Y. Montuno. Triangulating simple polygons and equivalent problems. ACM Trans. Graph., 3(2):153-174, 1984.
12. M. R. Garey, D. S. Johnson, F. P. Preparata, and R. E. Tarjan. Triangulating a simple polygon. Inform. Process. Lett., 7(4):175-179, 1978.
13. M. T. Goodrich. Planar separators and parallel polygon triangulation. J. Comput. System Sci., 51(3):374-389, 1995.
14. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 2:209-233, 1987.
15. J. Hershberger. Optimal parallel algorithms for triangulated simple polygons. Internat. J. Comput. Geom. Appl., 5:145-170, 1995.
16. D. G. Kirkpatrick, M. M. Klawe, and R. E. Tarjan. Polygon triangulation in O(n log log n) time with simple data structures. In Proc. 6th Annu. ACM Sympos. Comput. Geom., pages 34-43, 1990.
17. J. Matoušek. Derandomization in computational geometry. J. Algorithms, 20:545-580, 1996.
18. K. Mulmuley. A fast planar partition algorithm, I. J. Symbolic Comput., 10(3-4):253-280, 1990.
19. K. Mulmuley. Computational Geometry: An Introduction through Randomized Algorithms. Prentice-Hall, Englewood Cliffs, NJ, 1994.
20. R. Seidel. A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Comput. Geom. Theory Appl., 1(1):51-64, 1991.
21. R. E. Tarjan and C. J. Van Wyk. An O(n log log n)-time algorithm for triangulating a simple polygon. SIAM J. Comput., 17:143-178, 1988. Erratum in 17:106, 1988.