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

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

Trees are usually drawn planar, i.e. without any crossings. In this paper we investigate the area requirement of planar straight-line drawings of trees. A degree-d tree is one in which each node has at most d edges incident on it. Let T be a degree-d tree with n nodes, such that d = O(n δ), where δ < 1/2 is a constant. We show that T admits a planar straight-line grid drawing with area O(n) and with any prespecified 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.

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. Rao 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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Author information

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. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Garg, A., Rusu, A. (2003). Straight-Line Drawings of General Trees with Linear Area and Arbitrary Aspect Ratio. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_89

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  • DOI: https://doi.org/10.1007/3-540-44842-X_89

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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