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A More Practical Algorithm for Drawing Binary Trees in Linear Area with Arbitrary Aspect Ratio

机译:在任意纵横比的线性区域绘制二叉树的更实用算法

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Trees are usually drawn using planar straight-line drawings. 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 O(n 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.
机译:通常使用平面直线图绘制树木。提出了一种构造n节点二叉树的平面直线网格图的算法,该树的面积为O(n),且任何预先指定的纵横比在[n〜(-α),n〜α]范围内,其中0 ? α<1是任何常量,以O(n log n)时间表示。不幸的是,[1]的算法不适合实际使用。主要问题是,隐藏在“ Oh”表示法中的常数非常大(例如,可能高达3900)。在本文中,我们对算法做了一些实际的改进,使其适合实际使用。我们还针对该算法的较新版本进行了实验,该算法用于分别生成最多50、000和65、535个节点的随机生成的和完整的二叉树。我们的实验表明,它在实践中构造了面积有效的图形,面积分别是随机生成的和完整的二叉树的最大节点数的10倍和8倍。

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