The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Word Processing in Groups
Restricted rotation distance between binary trees
Information Processing Letters
A direct algorithm for restricted rotation distance
Information Processing Letters
Theoretical Computer Science
Efficient lower and upper bounds of the diagonal-flip distance between triangulations
Information Processing Letters
k-Restricted rotation distance between binary trees
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
Rotation distance is fixed-parameter tractable
Information Processing Letters
A metric for rooted trees with unlabeled vertices based on nested parentheses
Theoretical Computer Science
Root-restricted Kleenean rotations
Information Processing Letters
k-Restricted rotation with an application to search tree rebalancing
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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Restricted rotation distance between pairs of rooted binary trees quantifies differences in tree shape. Cleary exhibited a linear upper bound of 12n for the restricted rotation distance between two trees with n interior nodes, and a lower bound of (n - 1)/3 if the two trees satisfy a reduction condition. We obtain a significantly improved sharp upper bound of 4n - 8 for restricted rotation distance between two rooted binary trees with n interior nodes, and a significantly improved sharp lower bound of n - 2, again with the requirement that the trees satisfy a reduction condition. These improvements use work of Fordham to compute the word metric in Thompson's group F.