限制旋转距离的分布
Distributions of restricted rotation distances
摘要：
旋转距离度量有根有序二叉树之间的结构差异。结合面体的一维顶点是旋转图，其中表示树的两个顶点如果它们相差一个旋转，则由一条边连接。没有已知的有效算法来计算树之间的旋转距离，从而计算旋转图中的距离。限制允许旋转的允许位置引起了一些限制旋转距离的概念。允许在这样的位置的最小集合处的旋转给出了受限的旋转距离。有线性时间算法来计算限制旋转距离，其中只有两个允许旋转的位置发生。相关的限制旋转图有一个有效的距离算法。约束旋转距离与约简树对的大小存在线性上界和下界。在这里，我们通过实验研究预期的限制旋转的两棵树之间的距离随机选择的大小增加，并发现它通常位于一个狭窄的频带以及在较早的线性上限和下限。
英文摘要：
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a single rotation. There are no known efficient algorithms to compute rotation distance between trees and thus distances in rotation graphs. Limiting the allowed locations of where rotations are permitted gives rise to a number of notions of restricted rotation distances. Allowing rotations at a minimal such set of locations gives restricted rotation distance. There are linear-time algorithms to compute restricted rotation distance, where there are only two permitted locations for rotations to occur. The associated restricted rotation graph has an efficient distance algorithm. There are linear upper and lower bounds on restricted rotation distance with respect to the sizes of the reduced tree pairs. Here, we experimentally investigate the expected restricted rotation distance between two trees selected at random of increasing size and find that it lies typically in a narrow band well within the earlier proven linear upper and lower bounds.
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