Beta-skeletons have unbounded dilation

Computational Geometry: Theory and Applications

Volumn 23, Issue 1, 2002, Pages 43-52

  Eppstein, David ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Beta skeleton; Dilation; Fractal; Gabriel graph; Geometric graphs

Indexed keywords

EID: 31244438349     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(01)00055-4     Document Type: Article

References (15)

1. A.B. Amenta, M.W. Bern, D. Eppstein, The crust and the -skeleton: combinatorial curve reconstruction, Graphical Models Image Processing 60/2 (2) (1998) 125-135.
2. S. Cheng, Y. Xu, Approaching the largest β-skeleton within a minimum weight triangulation, in: Proc. 12th Symp. Comp. Geom., ACM, 1996, pp. 196-203.
3. L.P. Chew, There is a planar graph almost as good as the complete graph, in: Proc. 2nd Symp. Comp. Geom., ACM, 1986, pp. 169-177.
4. L.P. Chew, There are planar graphs almost as good as the complete graph, J. Comput. System Sci. 39 (1989) 205-219.
5. G. Das, D. Joseph, Which triangulations approximate the complete graph?, in: Proc. Int. Symp. Optimal Algorithms, Lecture Notes in Comp. Sci., Vol. 401, Springer, Berlin, 1989, pp. 168-192.
6. D.P. Dobkin, S.J. Friedman, K.J. Supowit, Delaunay graphs are almost as good as complete graphs, Discrete Comput. Geom. 5 (1990) 399-407.
7. D. Eppstein, Spanning trees and spanners, in: Handbook of Computational Geometry, Chapter 9, Elsevier, Amsterdam, 2000, pp. 425-461.
8. K.R. Gabriel, R.R. Sokal, A new statistical approach to geographic variation analysis, Systematic Zoology 18 (1969) 259-278.
9. J.M. Keil, Computing a subgraph of the minimum weight triangulation, Computational Geometry 4 (1994) 13-26.
10. J.M. Keil, C.A. Gutwin, The Delaunay triangulation closely approximates the complete Euclidean graph, in: Proc. 1st Worksh. Algorithms and Data Structures, Lecture Notes in Comp. Sci., Vol. 382, Springer, Berlin, 1989, pp. 47-56.
11. D.G. Kirkpatrick, J.D. Radke, A framework for computational morphology, in: Computational Geometry, North-Holland, Amsterdam, 1985, pp. 217-248.
12. T.-H. Su, R.-C. Chang, The fc-Gabriel graphs and their applications, in: Proc. Int. Symp. Algorithms, Lecture Notes in Comp. Sci., Vol. 450, Springer, Berlin, 1990, pp. 66-75.
13. R.C. Veitkamp, The y -neighborhood graph, Computational Geometry 1 (1992) 227-246.
14. C.A. Wang, B. Yang, A tight bound for beta-skeleton of minimum weight triangulations, in: Proc. 6th Int. Worksh. Algorithms and Data Structures, Lecture Notes in Comp. Sci., Vol. 1663, Springer, Berlin, 1999, pp. 265-275.
15. B.-T. Yang, A better subgraph of the minimum weight triangulation, Inform. Process. Lett. 56 (1995) 255-258.