Area-Efficient Drawings of Outerplanar Graphs

  • Ashim Garg
  • Adrian Rusu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

We show that an outerplanar graph G with n vertices and degree d admits a planar straight-line grid drawing with area O(dn1.48) in O(n) time. This implies that if d =o(n0.52), then G can be drawn in this fashion in o(n2) area.

References

  1. 1.
    Biedl, T.: Drawing outer-planar graphs in O(n log n) area. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 54–65. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Chan, T.M.: A near-linear area bound for drawing binary trees. Algorithmica 34(1), 1–13 (2002)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dujmovic, V., Wood, D.R.: Tree-partitions of k-trees with applications in graph layout. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 205–217. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Felsner, S., Liotta, G., Wismath, S.: Straight-line drawings on restricted integer grids in two and three dimensions. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 328–342. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Garg, A., Rusu, A.: Area-efficient drawings of outerplanar graphs. Technical Report No. 2003-11, Dept. Computer Sc. & Engg., Univ. at Buffalo, Buffalo (2003)Google Scholar
  7. 7.
    Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pp. 270–281 (1980)Google Scholar
  8. 8.
    Schnyder, W.: Embedding planar graphs on the grid. In: Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pp. 138–148 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ashim Garg
    • 1
  • Adrian Rusu
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

Personalised recommendations