2020/01/17 by Sean Cleary, Cleary, Sean, Roland Maio +1
Computer Science · #05C05 #05C12 #68R10 #Advanced Database Systems and Queries #Algorithms and Data Compression #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.2001.06407
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rotation distance between rooted binary trees is the minimum number of simple rotations needed to transform one tree into the other. Computing the rotation distance between a pair of rooted trees can be quickly reduced in cases where there is a common edge between the trees, or where a single rotation introduces a common edge. Tree pairs which do not have such a reduction are difficult tree pairs, where there is no generally known first step. Here, we describe efforts to count and estimate the number of such difficult tree pairs, and find that the fraction decreases exponentially fast toward zero. We also describe how knowing the number of distinct instances of the rotation distance problem is a helpful factor in making the computations more feasible.