On the dilation of delaunay triangulations of points in convex position

Proceedings of the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009

Volumn , Issue , 2009, Pages 161-164

  Cui, Shiliang ^a   Kanj, Iyad A ^b   Xia, Ge ^a  

^a LAFAYETTE COLLEGE   (United States)

^b DEPAUL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLETE GRAPHS; DELAU-NAY TRIANGULATIONS; EUCLIDEAN PLANES; FINITE SET; LOWER BOUNDS; STRETCH FACTOR; UPPER BOUND;

TRIANGULATION;

COMPUTATIONAL GEOMETRY;

EID: 84882943470     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. I. Altḧofer, G. Das, D. Dobkin, D. Joseph, and J. Soares. On sparse spanners of weighted graphs. Discrete & Comp. Geom., 9:81-100, 1993.
2. R. Benson. Euclidean Geometry and Convexity. McGraw-Hill, New York, 1966.
3. P. Bose. Open problems from CCCG 2007. Available at: http://erikdemaine. org/papers/CCCG2007Open/paper.pdf.
4. P. Bose, J. Gudmundsson, and M. Smid. Constructing plane spanners of bounded degree and low weight. Algorithmica, 42(3-4):249-264, 2005.
5. P. Bose, P. Morin, I. Stojmenovic, and J. Urrutia. Routing with guaranteed delivery in ad hoc wireless networks. Wireless Networks, 7(6):609-616, 2001.
6. P. Chew. There are planar graphs almost as good as the complete graph. JCSS, 39(2):205-219, 1989.
7. G. Das, P. Heffernan, and G. Narasimhan. Optimally sparse spanners in 3-dimensional Euclidean space. In SoCG, pages 53-62, 1993.
8. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algo- rithms and Applications, 3ed. Springer, 2007.
9. D. Dobkin, S. Friedman, and K. Supowit. Delaunay graphs are almost as good as complete graphs. In FOCS, pages 20-26, 1987.
10. D. Dobkin, S. Friedman, and K. Supowit. Delaunay graphs are almost as good as complete graphs. Discrete Comp. Geom., 5(4):399-407, 1990.
11. J. Gudmundsson, C. Levcopoulos, and G. Narasimhan. Fast greedy algorithms for constructing sparse geometric spanners. SIAM J. Comput., 31(5):1479-1500, 2002.
12. J. Keil and C. Gutwin. The Delaunay triangulation closely approximates the complete Euclidean graph. In WADS, pages 47-56, 1989.
13. J. Keil and C. Gutwin. Classes of graphs which approximate the complete Euclidean graph. Discrete & Comp. Geom., 7:13-28, 1992.
14. E. Kranakis, H. Singh, and J. Urrutia. Compass routing on geometric networks. In CCCG, pages 51-54, 1999.
15. C. Levcopoulos and A. Lingas. There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees. Algorithmica, 8(3):251-256, 1992.
16. X.-Y. Li, G. Calinescu, P.-J. Wan, and Y. Wang. Localized delaunay triangulation with application in Ad Hoc wireless networks. IEEE Transactions on Parallel and Distributed Systems., 14(10):1035- 1047, 2003.
17. G. Narasimhan and M. Smid. Geometric Spanner Networks. Cambridge University Press, 2007.
18. Y. Wang and X.-Y. Li. Localized construction of bounded degree and planar spanner for wireless ad hoc networks. Mobile Networks and Applications, 11(2):161-175, 2006.
19. A. C.-C. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM J. Comput., 11(4):721-736, 1982.