Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings
Chan, Timothy and Goodrich, Michael T. and Kosaraju, Rao and Tamassia, Roberto (1997) Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings. In: Symposium on Graph Drawing, GD '96, September 18-20, 1996, Berkeley, California, USA , pp. 63-75 (Official URL: http://dx.doi.org/10.1007/3-540-62495-3_38).
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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 aspekt 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(nlogn) and O(nloglogn), respectively, and we show that, at least in the case of upward drawings, our area bound is optimal to within constant factors.
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