Abstract
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.
This work is a consequence of the participation of Drs. Goodrich and Tamassia in the 1996 International Workshop on 3D Graph Drawing at Bellairs Research Inst. of McGill University.
This research was performed while the author was visiting the Center for Geometric Computing at Johns Hopkins University, and it was supported in part by by ARO under grant DAAH04-96-1-0013.
This research supported by NSF under Grants CCR-9300079 and CCR-9625289, and by ARO under grant DAAH04-96-1-0013.
This research supported by NSF under Grant CCR-9508545 and by ARO under grant DAAH04-96-1-0013.
This research supported by NSF under Grant CCR-9423847 and by ARO under grant DAAH04-96-1-0013.
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Chan, T., Kosaraju, S.R., Goodrich, M.T., Tamassia, R. (1997). Optimizing area and aspect ratio in straight-line orthogonal tree drawings. In: North, S. (eds) Graph Drawing. GD 1996. Lecture Notes in Computer Science, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62495-3_38
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DOI: https://doi.org/10.1007/3-540-62495-3_38
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