# Distributions of restricted rotation distances

Rotation distances measure the differences in structure between rooted ordered binary trees. There are no known efficient algorithms to compute rotation distance between trees, where rotations are permitted at any node. 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. 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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