Rotation Distance is Fixed-Parameter Tractable

TL;DR

This paper proves that computing the rotation distance between ordered rooted trees is fixed-parameter tractable, providing a new approach to a problem with no known polynomial-time solutions.

Contribution

It introduces a fixed-parameter tractability result for rotation distance, using kernelization to reduce trees to size bounded by 7k.

Findings

Rotation distance is fixed-parameter tractable.

Kernelization reduces trees to size 7k.

Provides a new algorithmic approach for ordered rooted trees.

Abstract

Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the rotation distance. The proof relies on the kernalization of the initial trees to trees with size bounded by 7k.