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Geometric Dilation of Geometric Networks

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  • First Online:
Encyclopedia of Algorithms

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Years and Authors of Summarized Original Work

  • 2006; Dumitrescu, Ebbers-Baumann, Grüne, Klein, Knauer, Rote

Geometric Dilation of Geometric Networks, Fig. 1
figure 75 figure 75

Minimum dilation embeddings of regular point sets

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Recommended Reading

  1. Aronov B, de Berg M, Cheong O, Gudmundsson J, Haverkort H, Vigneron A (2008) Sparse geometric graphs with small dilation. Comput Geom Theory Appl 40(3):207–219

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  2. Denne E, Sullivan JM (2004) The distortion of a knotted curve. http://www.arxiv.org/abs/math.GT/0409438

  3. Dumitrescu A, Ebbers-Baumann A, Grüne A, Klein R, Rote G (2006) On the geometric dilation of closed curves, graphs, and point sets. Comput Geom Theory Appl 36(1):16–38

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  4. Ebbers-Baumann A, Grüne A, Klein R (2006) On the geometric dilation of finite point sets. Algorithmica 44(2):137–149

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  5. Ebbers-Baumann A, Klein R, Knauer C, Rote G (2006) The geometric dilation of three points. Manuscript

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  6. Eppstein D (1999) Spanning trees and spanners. In: Sack J-R, Urrutia J (eds) Handbook of computational geometry, pp 425–461. Elsevier, Amsterdam

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  7. Gromov M (1981) Structures Métriques des Variétés Riemanniennes. Textes Math. CEDIX, vol 1. F. Nathan, Paris

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  8. Grüne A (2006) Geometric dilation and halving distance. Ph.D. thesis, Institut für Informatik I, Universität Bonn

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  9. Kuperberg K, Kuperberg W, Matousek J, Valtr P (1999) Almost tiling the plane with ellipses. Discrete Comput Geom 22(3):367–375

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  10. Kusner RB, Sullivan JM (1998) On distortion and thickness of knots. In: Whittington SG et al (eds) Topology and geometry in polymer science. IMA volumes in mathematics and its applications, vol 103. Springer, New York, pp 67–78

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  11. Narasimhan G, Smid M (2007) Geometric spanner networks. Cambridge University Press, Cambridge/New York

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Author information

Authors and Affiliations

  1. Institute for Computer Science, University of Bonn, Bonn, Germany

    Rolf Klein

Authors
  1. Rolf Klein
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Correspondence to Rolf Klein .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Klein, R. (2016). Geometric Dilation of Geometric Networks. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_166

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