An Algorithm to Construct Greedy Drawings of Triangulations

  • Patrizio Angelini
  • Fabrizio Frati
  • Luca Grilli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)


We show an algorithm to construct greedy drawings of every given triangulation.


  1. 1.
    Ben-Chen, M., Gotsman, C., Gortler, S.J.: Routing with guaranteed delivery on virtual coordinates. In: CCCG 2006 (2006)Google Scholar
  2. 2.
    Ben-Chen, M., Gotsman, C., Wormser, C.: Distributed computation of virtual coordinates. In: Erickson, J. (ed.) SoCG 2007, pp. 210–219. ACM Press, New York (2007)Google Scholar
  3. 3.
    Dhandapani, R.: Greedy drawings of triangulations. In: Huang, S.-T. (ed.) SODA 2008, pp. 102–111. SIAM, Philadelphia (2008)Google Scholar
  4. 4.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Kleinberg, R.: Geographic routing using hyperbolic space. In: INFOCOM 2007, pp. 1902–1909. IEEE, Los Alamitos (2007)Google Scholar
  6. 6.
    Knaster, B., Kuratowski, C., Mazurkiewicz, C.: Ein beweis des fixpunktsatzes fur n dimensionale simplexe. Fundamenta Mathematicae 14, 132–137 (1929)MATHGoogle Scholar
  7. 7.
    Leighton, T., Moitra, A.: Some results on greedy embeddings in metric spaces. In: FOCS 2008 (2008)Google Scholar
  8. 8.
    Papadimitriou, C.H., Ratajczak, D.: On a conjecture related to geometric routing. Theor. Comput. Sci. 344(1), 3–14 (2005)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Rao, A., Papadimitriou, C.H., Shenker, S., Stoica, I.: Geographic routing without location information. In: Johnson, D.B., Joseph, A.D., Vaidya, N.H. (eds.) MOBICOM 2003, pp. 96–108. ACM Press, New York (2003)Google Scholar
  10. 10.
    Schnyder, W.: Embedding planar graphs on the grid. In: SODA 1990, pp. 138–148. SIAM, Philadelphia (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Fabrizio Frati
    • 1
  • Luca Grilli
    • 2
  1. 1.Dipartimento di Informatica e AutomazioneRoma Tre UniversityItaly
  2. 2.Dipartimento di Ingegneria Elettronica e dell’InformazionePerugia UniversityItaly

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