Abstract
Computing the Delaunay triangulation of n points is well known to have an Ω(n log n) lower bound. Researchers have attempted to break that bound in special cases where additional information is known.
The French team was partially supported by Picasso French-Spanish collaboration program. The Spanish team was partially supported by CUR Gen. Cat. 1999SGR00356, Proyecto DGES-MEC PB98-0933 and Acción Integrada Francia-España HF99-112.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
J.-D. Boissonnat and M. Teillaud. On the randomized construction of the Delaunay tree. Theoret. Comput. Sci., 112:339–354, 1993.
B. Chazelle. Triangulating a simple polygon in linear time. Discrete Comput. Geom., 6(5):485–524, 1991.
B. Chazelle. An optimal algorithm for intersecting three-dimensional convex poly-hedra. SIAM J. Comput., 21(4):671–696, 1992.
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.
L. P. Chew and S. Fortune. Sorting helps for Voronoi diagrams. Algorithmica, 18:217–228, 1997.
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.
L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387–421, 1989.
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, Aug. 1997.
M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, 1997.
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.
H. Djidjev and A. Lingas. On computing Voronoi diagrams for sorted point sets. Internat. J. Comput. Geom. Appl., 5:327–337, 1995.
L. J. Guibas, D. E. Knuth, and M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica, 7:381–413, 1992.
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.
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.
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, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chazelle, B., Devillers, O., Hurtado, F., Mora, M., Sacristán, V., Teillaud, M. (2001). Splitting a Delaunay Triangulation in Linear Time. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_26
Download citation
DOI: https://doi.org/10.1007/3-540-44676-1_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42493-2
Online ISBN: 978-3-540-44676-7
eBook Packages: Springer Book Archive