Restricted rotation distance between k-ary trees
Vol. 27, no. 1, pp. 19-33, 2023. Regular paper.
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.

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Submitted: June 2022.
Reviewed: July 2022.
Revised: December 2022.
Accepted: February 2023.
Final: February 2023.
Published: February 2023.
Communicated by Giuseppe Liotta
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