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Area-Efficient Order-Preserving Planar Straight-Line Drawings of Ordered Trees

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Computing and Combinatorics (COCOON 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

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Abstract

Ordered trees are generally drawn using order-preserving planar straight-line grid drawings. We therefore investigate the arearequirements of such drawings, and present several results: Let T be an ordered tree with n nodes. Then:

  • T admits an order-preserving planar straight-line grid drawing with O(n log n) area.

  • If T is a binary tree, then T admits an order-preserving planar straight-line grid drawing with O(n log log n) area.

  • If T is a binary tree, then T admits an order-preserving upward planar straight-line grid drawing with optimal O(n log n) area.

We also study the problem of drawing binary trees with user-specified arbitrary aspect ratios. We show that an ordered binary tree T with n nodes admits an order-preserving planar straight-line grid drawing Γ with width O(A + log n), height O((n/A) logA), and area O((A + log n)(n/A) logA) = O(n log n), where 2 ≤ A ≤ n is any user-specified number. Also note that all the drawings mentioned above can be constructed in O(n) time.

Research supported by NSF CAREER Award IIS-9985136 and NSF CISE Research Infrastructure Award No. 0101244.

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References

  1. T. Chan, M. Goodrich, S. R. Kosaraju, and R. Tamassia. Optimizing area and aspect ratio in straight-line orthogonal tree drawings. Comput. Geom. Theory Appl., 23:153–162, 2002.

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  5. A. Garg and A. Rusu. Area-efficient order-preserving planar straight-line drawings of ordered trees. Technical Report 2003-05, Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, 2003.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, 14260

    Ashim Garg & Adrian Rusu

Authors
  1. Ashim Garg
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  2. Adrian Rusu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

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Garg, A., Rusu, A. (2003). Area-Efficient Order-Preserving Planar Straight-Line Drawings of Ordered Trees. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_48

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  • DOI: https://doi.org/10.1007/3-540-45071-8_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

  • eBook Packages: Springer Book Archive

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