Optimizing area and aspect ratio in straight-line orthogonal tree drawings
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We investigate the problem of drawing an arbitrary n-node binary tree orthogonally in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as being O(1) or sometimes even an arbitrary parameter. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call “subtree separation.” We investigate both upward and non-upward drawings, achieving area bounds of O(n log n) and O(n log log n), respectively, and we show that, at least in the case of upward drawings, our area bound is optimal to within constant factors.
- R. P. Brent and H. T. Kung. On the area of binary tree layouts. Inform. Process. Lett., 11:521–534, 1980. CrossRef
- P. Crescenzi, G. Di Battista, and A. Piperno. A note on optimal area algorithms for upward drawings of binary trees. Comput. Geom. Theory Appl., 2:187–200, 1992.
- P. Crescenzi and A. Piperno. Optimal-area upward drawings of AVL trees. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science, pages 307–317. Springer-Verlag, 1995.
- G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Algorithms for drawing graphs: an annotated bibliography. Comput. Geom. Theory Appl., 4:235–282, 1994.
- A. Garg, M. T. Goodrich, and R. Tamassia. Area-efficient upward tree drawings. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 359–368, 1993.
- C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proc. 21st Annu. IEEE Sympos. Found. Comput. Sci., pages 270–281, 1980.
- C. E. Leiserson. Area-efficient graph layouts (for VLSI). ACM Doctoral Dissertation Award Series. MIT Press, Cambridge, MA, 1983.
- E. Reingold and J. Tilford. Tidier drawing of trees. IEEE Trans. Softw. Eng., SE-7(2):223–228, 1981.
- Y. Shiloach. Arrangements of Planar Graphs on the Planar Lattice. PhD thesis, Weizmann Institute of Science, 1976.
- L. Trevisan. A note on minimum-area upward drawing of complete and Fibonacci trees. Information Processing Letters, 57(5):231–236, 1996. CrossRef
- L. Valiant. Universality considerations in VLSI circuits. IEEE Trans. Comput., C-30(2):135–140, 1981.
- Optimizing area and aspect ratio in straight-line orthogonal tree drawings
- Book Title
- Graph Drawing
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- Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996 Proceedings
- pp 63-75
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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