Rotation distance between rooted binary trees measures the extent of similarity of two trees with ordered leaves. There are no known polynomial-time algorithms for computing rotation distance. If there are common edges or immediately changeable edges between a pair of trees, the rotation distance problem breaks into smaller subproblems. The number of crossings or conflicts of a tree pair also gives some measure of the extent of similarity of two trees. Here we describe the distribution of common edges and immediately changeable edges between randomly selected pairs of trees via computer experiments, and examine the distribution of the amount of conflicts between such pairs.
"Expected conflicts in pairs of rooted binary trees." Involve 6 (3) 323 - 332, 2013. https://doi.org/10.2140/involve.2013.6.323