关于旋转距离问题的困难树对计数
Counting difficult tree pairs with respect to the rotation distance problem
摘要：
有根二叉树之间的旋转距离是将一棵树转换为另一棵树所需的最小简单旋转次数。在树之间存在公共边的情况下，或者在单个旋转引入公共边的情况下，可以快速减少计算一对有根树之间的旋转距离。不具有这样的约简的树对是困难的树对，其中没有通常已知的第一步。在这里，我们描述了努力计数和估计这样的困难的树对的数量，并发现该分数呈指数快速下降到零。我们还描述了如何知道旋转距离问题的不同实例的数量是一个有帮助的因素，使计算更可行。
英文摘要：
Rotation distance between rooted binary trees is the minimum number of simple rotations needed to transform one tree into the other. Computing the rotation distance between a pair of rooted trees can be quickly reduced in cases where there is a common edge between the trees, or where a single rotation introduces a common edge. Tree pairs which do not have such a reduction are difficult tree pairs, where there is no generally known first step. Here, we describe efforts to count and estimate the number of such difficult tree pairs, and find that the fraction decreases exponentially fast toward zero. We also describe how knowing the number of distinct instances of the rotation distance problem is a helpful factor in making the computations more feasible.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
