On the rotation distance of binary trees
Information Processing Letters
On the upper bound on the rotation distance of binary trees
Information Processing Letters
Restricted rotation distance between binary trees
Information Processing Letters
Bounding restricted rotation distance
Information Processing Letters
Efficient lower and upper bounds of the diagonal-flip distance between triangulations
Information Processing Letters
Rotational tree structures on binary trees and triangulations
Acta Cybernetica
Note: Refined upper bounds for right-arm rotation distances
Theoretical Computer Science
Effective splaying with restricted rotations
International Journal of Computer Mathematics
Weak associativity and restricted rotation
Information Processing Letters
A metric for rooted trees with unlabeled vertices based on nested parentheses
Theoretical Computer Science
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The restricted rotation distancedR(S, T) between two binary trees S, T of n vertices is the minimum number of rotations by which S can be transformed into T, where rotations can only take place at the root of the tree, or at the right child of the root. A sharp upper bound dR(S, T) ≤ 4n – 8 is known, based on the word metric of Thompson's group. We refine this bound to a sharp dR(S, T) ≤ 4n – 8 – ρS – ρT, where ρS and ρT are the numbers of vertices in the rightmost vertex chains of the two trees, by means of a very simple transformation algorithm based on elementary properties of trees. We then generalize the concept of restricted rotation to k-restricted rotation, by allowing rotations to take place at all the vertices of the highest k levels of the tree. For k = 2 we show that not much is gained in the worst case, although the classical problem of rebalancing an AVL tree can be solved efficiently, in particular rebalancing after vertex deletion requires O(log n) rotations as in the standard algorithm. Finding significant bounds and applications for k ≥ 3 is open.