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Upward drawings of search trees

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Graph-Theoretic Concepts in Computer Science (WG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1197))

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Scienze dell'Informazione, Via Salaria 113, 00198, Roma

    P. Crescenzi & P. Penna

Authors
  1. P. Crescenzi
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  2. P. Penna
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Editor information

Fabrizio d'Amore Paolo Giulio Franciosa Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Crescenzi, P., Penna, P. (1997). Upward drawings of search trees. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_11

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  • DOI: https://doi.org/10.1007/3-540-62559-3_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62559-9

  • Online ISBN: 978-3-540-68072-7

  • eBook Packages: Springer Book Archive

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