he restricted rotation distancedR (S, T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T, where rotations take place at the root of S, or at the right child of the root. A sharp upper bound dR (S, T) ≤ 4 n - 8 is known, based on group theory [S. Cleary, J. Taback, Bounding restricted rotation distance, Information Processing Letters 88 (5) (2003) 251-256]. We refine this bound to a sharp dR (S, T) ≤ 4 n - 8 - ρS - ρT, where ρS and ρT are the numbers of vertices in the rightmost vertex chains of the two trees, using an elementary transformation algorithm. We then generalize the concept to k-restricted rotation, by allowing rotations to take place at all the vertices of the highest k levels of the tree, and study the new distance for k = 2. The case k ≥ 3 is essentially open.

### K-restricted rotation distance between binary trees

#### Abstract

he restricted rotation distancedR (S, T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T, where rotations take place at the root of S, or at the right child of the root. A sharp upper bound dR (S, T) ≤ 4 n - 8 is known, based on group theory [S. Cleary, J. Taback, Bounding restricted rotation distance, Information Processing Letters 88 (5) (2003) 251-256]. We refine this bound to a sharp dR (S, T) ≤ 4 n - 8 - ρS - ρT, where ρS and ρT are the numbers of vertices in the rightmost vertex chains of the two trees, using an elementary transformation algorithm. We then generalize the concept to k-restricted rotation, by allowing rotations to take place at all the vertices of the highest k levels of the tree, and study the new distance for k = 2. The case k ≥ 3 is essentially open.
##### Scheda breve Scheda completa Scheda completa (DC)
2007
Luccio, Fabrizio; A., MESA ENRIQUES; Pagli, Linda
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11568/205779`
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