On the rotation distance in the lattice of binary trees
Information Processing Letters
On the rotation distance of binary trees
Information Processing Letters
On the upper bound on the rotation distance of binary trees
Information Processing Letters
A shortest path metric on unlabeled binary trees
Pattern Recognition Letters
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
Finding paths in the rotation graph of binary trees
Finding paths in the rotation graph of binary trees
Right-arm rotation distance between binary trees
Information Processing Letters
Bounding restricted rotation distance
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
Effective splaying with restricted rotations
International Journal of Computer Mathematics
Weak associativity and restricted rotation
Information Processing Letters
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 measures differences in tree shape and is related to rotation distance. In restricted rotation distance, the rotations used to transform the trees are allowed to be only of two types. Restricted rotation distance is larger than rotation distance, since there are only two permissible locations to rotate, but is much easier to compute and estimate. We obtain linear upper and lower bounds for restricted rotation distance in terms of the number of interior nodes in the trees. Further, we describe a linear-time algorithm for estimating the restricted rotation distance between two trees and for finding a sequence of rotations which realizes that estimate. The methods use the metric properties of the abstract group known as Thompson's group F.