Dilation of Geometric Networks
Living reference work entry
First Online:
Received:
Accepted:
DOI: https://doi.org/10.1007/978-3-642-27848-8_111-2
Years and Authors of Summarized Original Work
2005; Ebbers-Baumann, Grüne, Karpinski, Klein, Knauer, Lingas
Problem Definition
Notations
Let
G = (
V,
E) be a plane geometric network, whose vertex set
V is a finite set of point sites in
\(\mathbb{R}^{2}\)
Keywords
Detour Spanning ratio Stretch factorThis is a preview of subscription content, log in to check access.
Recommended Reading
- 1.Aronov B, de Berg M, Cheong O, Gudmundsson J, Haverkort H, Vigneron A (2005) Sparse geometric graphs with small dilation. In: Deng X, Du D (eds) Algorithms and computation: proceedings of the 16th international symposium (ISAAC 2005), Sanya. LNCS, vol 3827, pp 50–59. Springer, BerlinCrossRefGoogle Scholar
- 2.Das G, Joseph D (1989) Which triangulations approximate the complete graph? In: Proceedings of the international symposium on optimal algorithms, Varna. LNCS, vol 401, pp 168–192. Springer, BerlinGoogle Scholar
- 3.Dobkin DP, Friedman SJ, Supowit KJ (1990) Delaunay graphs are almost as good as complete graphs. Discret Comput Geom 5:399–407MathSciNetCrossRefGoogle Scholar
- 4.Ebbers-Baumann A, Gruene A, Karpinski M, Klein R, Knauer C, Lingas A (2007) Embedding point sets into plane graphs of small dilation. Int J Comput Geom Appl 17(3):201–230CrossRefGoogle Scholar
- 5.Eppstein D, The geometry junkyard. http://www.ics.uci.edu/~eppstein/junkyard/dilation-free/
- 6.Eppstein D (1999) Spanning trees and spanners. In: Sack J-R, Urrutia J (eds) Handbook of computational geometry. Elsevier, Amsterdam, pp 425–461Google Scholar
- 7.Eppstein D, Wortman KA (2005) Minimum dilation stars. In: Proceedings of the 21st ACM symposium on computer geometry (SoCG), Pisa, pp 321–326Google Scholar
- 8.Hillar CJ, Rhea DL (2006) A result about the density of iterated line intersections. Comput Geom Theory Appl 33(3):106–114MATHMathSciNetCrossRefGoogle Scholar
- 9.Ismailescu D, Radoičić R (2004) A dense planar point set from iterated line intersections. Comput Geom Theory Appl 27(3):257–267MATHCrossRefGoogle Scholar
- 10.Keil JM, Gutwin CA (1992) The Delaunay triangulation closely approximates the complete Euclidean graph. Discret Comput Geom 7:13–28MATHMathSciNetCrossRefGoogle Scholar
- 11.Klein R, Kutz M, Penninger R (2015) Most finite point sets have dilation > 1. Discret Comput Geom 53:80–106MathSciNetCrossRefGoogle Scholar
- 12.Narasimhan G, Smid M (2007) Geometric spanner networks. Cambridge University Press, Cambridge/New YorkMATHCrossRefGoogle Scholar
Copyright information
© Springer Science+Business Media New York 2014