On the rotation distance between binary trees

TL;DR

This paper introduces combinatorial techniques to compute the rotation distance between binary trees and demonstrates that for each size n, there are trees at a distance close to 2n, specifically 2n - O(sqrt(n)).

Contribution

It develops new combinatorial methods for calculating rotation distances and establishes bounds on the maximum distance between trees of a given size.

Findings

Existence of tree pairs at distance 2n - O(sqrt(n)) for size n.

New combinatorial methods for rotation distance computation.

Connection between binary trees and polygon triangulations.

Abstract

We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at distance 2n - O(sqrt(n)).