Upward drawings of search trees

Extended abstract
  • P. Crescenzi
  • P. Penna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)


We prove that any logarithmic binary tree admits a linear-area straight-line strictly-upward planar grid drawing (in short, upward drawing), that is, a drawing in which (a) each edge is mapped into a single straight-line segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates. Informally, a logarithmic tree has the property that the height of any (sufficiently high) subtree is logarithmic with respect to the number of nodes. As a consequence, we have that k-balanced trees, red-black trees, and BB[α]-trees admit linear-area upward drawings. We then generalize our results to logarithmic m-ary trees: as an application, we have that B-trees admit linear-area upward drawings.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • P. Crescenzi
    • 1
  • P. Penna
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneRoma

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