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Straight-Line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio

(Extended Abstract)
  • Ashim Garg
  • Adrian Rusu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

Trees are usually drawn planar, i.e. without any crossings. In this paper, we investigate the area requirement of (non-upward) planar straight-line grid drawings of binary trees. Let T be a binary tree with n nodes. We show that T admits a planar straight-line grid drawing with area O(n) and with any pre-specified aspect ratio in the range [1, n α ], where α is a constant such that 0 ≤ α < 1. We also show that such a drawing can be constructed in O(n log n) time.

References

  1. 1.
    T. Chan, M. Goodrich, S. Rao Kosaraju, and R. Tamassia. Optimizing area and aspect ratio in straight-line orthogonal tree drawings. Comput. Geom. Theory Appl. to appear. Prel. version in Proc. Graph Drawing’96, LNCS, vol. 1190, pp. 63–75.Google Scholar
  2. 2.
    P. Crescenzi, G. Di Battista, and A. Piperno. A note on optimal area algorithms for upward drawings of binary trees. Comput. Geom. Theory Appl., 2:187–200, 1992.zbMATHGoogle Scholar
  3. 3.
    P. Crescenzi, P. Penna, and A. Piperno. Linear-area upward drawings of AVL trees. Comput. Geom. Theory Appl., 9:25–42, 1998.zbMATHMathSciNetGoogle Scholar
  4. 4.
    G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing. Prentice Hall, Upper Saddle River, NJ, 1999.zbMATHCrossRefGoogle Scholar
  5. 5.
    A. Garg, M. T. Goodrich, and R. Tamassia. Planar upward tree drawings with optimal area. Internat. J. Comput. Geom. Appl., 6:333–356, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pages 270–281, 1980.Google Scholar
  7. 7.
    C.-S. Shin, S.K. Kim, S.-H. Kim, and K.-Y. Chwa. Area-efficient algorithms for straight-line tree drawings. Comput. Geom. Theory Appl., 15:175–2002, 2000.zbMATHMathSciNetGoogle Scholar
  8. 8.
    L. Trevisan. A note on minimum-area upward drawing of complete and Fibonacci trees. Inform. Process. Lett., 57(5):231–236, 1996.CrossRefMathSciNetGoogle Scholar
  9. 9.
    L. Valiant. Universality considerations in VLSI circuits. IEEE Trans. Comput., C-30(2):135–140, 1981.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

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

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