Abstract
Trees are usually drawn using planar straight-line drawings. [1] presented an algorithm for constructing a planar straight-line grid drawing of an n-node binary tree with area O(n) and any pre-specified aspect ratio in the range [n − α,n α], where 0 ≤ α < 1 is any constant, in \(\mathcal{O}(n {\rm log}n)\) time. Unfortunately, the algorithm of [1] is not suitable for practical use. The main problem is that the constant hidden in the “Oh” notation for area is quite large (e.g., it can be as large as 3900).
In this paper, we have made several practical improvements to the algorithm, which make it suitable for practical use. We have also conducted experiments on this newer version of the algorithm for randomly-generated and complete binary trees with up to 50,000, and 65,535 nodes, respectively. Our experiments show that it constructs area-efficient drawings in practice, with area at most 10 times and 8 times the number of nodes for randomly-generated and complete binary trees, respectively.
Research supported by NSF CAREER Award IIS-9985136, NSF CISE Research Infrastructure Award No. 0101244, and Mark Diamond Research Grant No. 13-Summer-2003 from GSA of The State University of New York.
Chapter PDF
Similar content being viewed by others
References
Garg, A., Rusu, A.: Straight-line drawings of binary trees with linear area and arbitrary aspect ratio. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 320–331. Springer, Heidelberg (2002)
Garg, A., Rusu, A.: A more practical algorithm for drawing binary trees in linear area with arbitrary aspect ratio. Technical Report No. 2003-12, Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY (2003)
Valiant, L.: Universality considerations in VLSI circuits. IEEE Trans. Comput. C-30(2), 135–140 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Garg, A., Rusu, A. (2004). A More Practical Algorithm for Drawing Binary Trees in Linear Area with Arbitrary Aspect Ratio. In: Liotta, G. (eds) Graph Drawing. GD 2003. Lecture Notes in Computer Science, vol 2912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24595-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-24595-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20831-0
Online ISBN: 978-3-540-24595-7
eBook Packages: Springer Book Archive