Lower Bounds on the Rotation Distance of Binary Trees

Luccio, Fabrizio and Mesa Enriquez, Antonio and Pagli, Linda (2010) Lower Bounds on the Rotation Distance of Binary Trees. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

The rotation distance d(S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T. While it is known that d(S,T) <= 2n-6, a well known conjecture states that there are trees for which this bound is sharp for any value of n >= 11. We are unable to prove the conjecture, but we give here some simple criteria for lower bound evaluation, leading for example to individuate some ``regular'' tree structures for which d(S,T) = 3n/2-O(1), or d(S,T) = 5n/3-O(1).

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