Splitting a delaunay triangulation in linear time

Algorithmica (New York)

Volumn 34, Issue 1, 2002, Pages 39-46

  Chazelle, B ^a   Devillers, O ^b   Hurtado, F ^c   Mora, M ^c   Sacristan V ^c   Teillaud, M ^b  

^a Princeton University   (United States)

^b INRIA   (France)

^c UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Computational geometry; Delaunay triangulation; Randomized algorithms; Voronoi diagrams

Indexed keywords

ALGORITHMS; GRAPH THEORY; SET THEORY;

RANDOMIZED ALGORITHMS;

COMPUTATIONAL METHODS;

EID: 0141957143     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-002-0939-8     Document Type: Article

References (20)

1. A. Aggarwal, L. J. Guibas, J. Saxe, and P. W. Shor. A linear-time algorithm for computing the Voronoi diagram of a convex polygon. Discrete Comput. Geom., 4(6):591-604, 1989.
2. N. M. Amato, M. T. Goodrich, and E. A. Ramos. Linear-time triangulation of a simple polygon made easier via randomization. In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 201-212, 2000.
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., 8:51-71, 1992.
4. J.-D. Boissonnat, O. Devillers, M. Teillaud, and M. Yvinec. Triangulations in CGAL. In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 11-18, 2000.
5. J.-D. Boissonnat and M. Teillaud. On the randomized construction of the Delaunay tree. Theoret. Comput. Sci., 112:339-354, 1993.
6. B. Chazelle. Triangulating a simple polygon in linear time. Discrete Comput. Geom., 6(5):485-524, 1991.
7. B. Chazelle. An optimal algorithm for intersecting three-dimensional convex polyhedra. SIAM J. Comput., 21(4):671-696, 1992.
8. L. P. Chew. Building Voronoi diagrams for convex polygons in linear expected time. Technical Report PCS-TR90-147, Dept. Math. Comput. Sci., Dartmouth College, Hanover, NH, 1986.
9. L. P. Chew and S. Fortune. Sorting helps for Voronoi diagrams. Algorithmica, 18:217-228, 1997.
10. F. Chin, J. Snoeyink, and C. A. Wang. Finding the medial axis of a simple polygon in linear time. Discrete Comput. Geom., 21(3):405-420, 1999.
11. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
12. M. de Berg, O. Devillers, K. Dobrindt, and O. Schwarzkopf. Computing a single cell in the overlay of two simple polygons. Inform. Process. Lett., 63(4):215-219, August 1997.
13. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, 1997.
14. O. Devillers. Randomization yields simple O (n log* n) algorithms for difficult Ω (n) problems. Internat. J. Comput. Geom. Appl., 2(1):97-111, 1992.
15. H. Djidjev and A. Lingas. On computing Voronoi diagrams for sorted point sets. Internat. J. Comput. Geom. Appl., 5:327-337, 1995.
16. L. J. Guibas, D. E. Knuth, and M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica, 7:381-413, 1992.
17. R. Klein and A. Lingas. A linear-time randomized algorithm for the bounded Voronoi diagram of a simple polygon. Internat. J. Comput. Geom. Appl., 6:263-278, 1996.
18. 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.
19. R. Seidel. Backwards analysis of randomized geometric algorithms. In J. Pach, editor, New Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics, pages 37-68. Springer-Verlag, New York, 1993.
20. J. Snoeyink and M. van Kreveld. Good orders for incremental (re)constructions. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 400-402, 1997.