Optimizing area and aspect ratio in straight-line orthogonal tree drawings

  • Timothy Chan
  • S. Rao Kosaraju
  • Michael T. Goodrich
  • Roberto Tamassia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)


We investigate the problem of drawing an arbitrary n-node binary tree orthogonally in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call “subtree separation.” We investigate both upward and non-upward drawings, achieving area bounds of O(n log n) and O(n log log n), respectively, and we show that, at least in the case of upward drawings, our area bound is optimal to within constant factors.


Aspect Ratio Binary Tree Polygonal Chain Aesthetic Criterion Geometric Computing 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Timothy Chan
    • 1
  • S. Rao Kosaraju
  • Michael T. Goodrich
    • 1
  • Roberto Tamassia
    • 2
  1. 1.Center for Geometric Computing Dept. of Computer ScienceJohns Hopkins Univ.USA
  2. 2.Center for Geometric Computing Dept. of Computer ScienceBrown Univ.USA

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