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Optimizing area and aspect ratio in straight-line orthogonal tree drawings

机译:在直线正交树图中优化面积和纵横比

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We investigate the problem of drawing an arbitrary n-node binary tree orthogonally and upwardly 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 a fixed constant or a parameter under the user's control. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call "subtree separation". Our drawings require O(n log n) area, which we show is optimal to within constant factors in the worst case (i.e. there are trees that need Ω(n log n) area for any upward orthogonal straight-line drawing with good aspect ratio). An improvement for non-upward drawings is briefly mentioned.
机译:我们研究了使用直线边缘在整数网格中正交向上绘制任意n节点二叉树的问题。我们表明,一个人可以同时实现良好的区域边界,同时还允许在用户的控制下将纵横比选择为固定常数或参数。另外,我们表明,人们还可以实现另一种理想的审美标准,我们称之为“子树分离”。我们的工程图需要O(n log n)面积,这表明在最坏的情况下,该常数最适合在恒定因子范围内(例如,对于任何具有良好长宽比的向上正交直线图,树木都需要Ω(n log n)面积)。简要提到了非上图的改进。

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