Optimal-area upward drawings of AVL trees

  • P. Crescenzi
  • A. Piperno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)


We prove that any AVL tree admits a linear-area planar straight-line grid strictly-upward drawing, that is, a drawing in which (a) no two edges intersect, (b) each edge is mapped into a single straight-line segment, (c) each node is mapped into a point with integer coordinates, and (d) each node is placed below its parent.


Binary Tree Computational Geometry Short Side Longe Side Complete Binary Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G.M. Adelson-Velskii and E.M. Landis. An algorithm for the organization of information. Soviet Math. Dokl., 3:1259–1262, 1962.Google Scholar
  2. 2.
    P. Crescenzi, G. Di Battista, and A. Piperno. A note on optimal area algorithms for upward drawings of binary trees. Computational Geometry: Theory and Applications, 2:187–200, 1992.Google Scholar
  3. 3.
    G. Di Battista, P. Eades, and R. Tamassia. Algorithms for drawing graphs: an annotated bibliography. Computational Geometry: Theory and Applications, to appear. A preliminary version is available via anonymous ftp from, gdbiblio.tex.Z and in /pub/papers/compgeo.Google Scholar
  4. 4.
    P. Eades, T. Lin, and X. Lin. Minimum size h-v drawings. In Proc. Int. Workshop AVI '92, pages 386–394, 1992.Google Scholar
  5. 5.
    Y. Horibe. An Entropy View of Fibonacci Trees. Fibonacci Quarterly, 20:168–178, 1982.Google Scholar
  6. 6.
    Y. Horibe. Notes on Fibonacci Trees and Their Optimality. Fibonacci Quarterly, 21:118–128, 1983.Google Scholar
  7. 7.
    D.E. Knuth. The Art of Computer Programming, Addison Wesley, 1975.Google Scholar
  8. 8.
    A. Garg, M.T. Goodrich, and R. Tamassia. Area-efficient upward tree drawing. In Proc. ACM Symp. on Computational Geometry, pages 359–368, 1993.Google Scholar
  9. 9.
    R.L. Graham, D.E. Knuth, and O. Patashnik. Concrete Mathematics, Addison Wesley, 1989.Google Scholar
  10. 10.
    E. Reingold and J. Tilford. Tidier drawing of trees. IEEE Trans. on Software Engineering, SE-7:223–228, 1981.Google Scholar
  11. 11.
    K.J. Supowit and E. Reingold. The complexity of drawing trees nicely. Acta Information, 18:377–392, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • P. Crescenzi
    • 1
  • A. Piperno
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneUniversità degli Studi di Roma “La Sapienza”Roma

Personalised recommendations