Restricted rotation distance between k-ary trees

Abstract

We study restricted rotation distance between ternary and higher-valence trees using approaches based upon generalizations of Thompson's group $F$. We obtain bounds and a method for computing these distances exactly in linear time, as well as a linear-time algorithm for computing rotations needed to realize these distances. Unlike the binary case, the higher-valence notions of rotation distance do not give Tamari lattices, so there are fewer tools for analysis in the higher-valence settings. Higher-valence trees arise in a range of database and filesystem applications where balance is important for efficient performance.