Small Area Drawings of Outerplanar Graphs

(Extended Abstract)
  • Giuseppe Di Battista
  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

We show three linear time algorithms for constructing planar straight-line grid drawings of outerplanar graphs. The first and the second algorithm are for balanced outerplanar graphs. Both require linear area. The drawings produced by the first algorithm are not outerplanar while those produced by the second algorithm are. On the other hand, the first algorithm constructs drawings with better angular resolution. The third algorithm constructs outerplanar drawings of general outerplanar graphs with O(n1.48) area. Further, we study the interplay between the area requirements of the drawings of an outerplanar graph and the area requirements of a special class of drawings of its dual tree.

References

  1. 1.
    Biedl, T.: Drawing outer-planar graphs in O(n logn) area. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 54–65. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bose, P.: On embedding an outer-planar graph in a point set. In: Di Battista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 25–36. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Chan, T.M.: A near-linear area bound for drawing binary trees. Algorithmica 34(1) (2002)Google Scholar
  4. 4.
    Chrobak, M., Payne, T.H.: A linear-time algorithm for drawing a planar graph on a grid. IPL 54(4), 241–246 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Upper Saddle River (1999)MATHGoogle Scholar
  7. 7.
    Felsner, S., Liotta, G., Wismath, S.K.: Straight-line drawings on restricted integer grids in two and three dimensions. J. Graph Algorithms Appl. 7(4), 363–398 (2003)MATHMathSciNetGoogle Scholar
  8. 8.
    Garg, A., Rusu, A.: Straight-line drawings of binary trees with linear area and arbitrary aspect ratio. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 320–331. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Garg, A., Rusu, A.: Area-efficient planar straight-line grid drawings of outerplanar graphs. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 129–134. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Gritzmann, P., Mohar, B., Pach, J., Pollack, R.: Embedding a planar triangulation with vertices at specified points. Amer. Math. Monthly 98(2), 165–166 (1991)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pp. 270–281 (1980)Google Scholar
  12. 12.
    Malitz, S., Papakostas, A.: On the angular resolution of planar graphs. SIAM J. Discrete Math. 7, 172–183 (1994)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Schnyder, W.: Embedding planar graphs on the grid. In: Proc. 1st ACM-SIAM Sympos. Discr. Alg., pp. 138–148 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità di Roma Tre 

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