Enumeration and Succinct Encoding of AVL Trees
International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) 2024
Jeremy Chizewer*, Stephen Melczer*, J. Ian Munro*, Ava Pun*
We use a novel decomposition to create succinct data structures - supporting a wide range of operations on static trees in constant time - for a variety of tree classes, extending results of Munro, Nicholson, Benkner, and Wild. Motivated by the class of AVL trees, we further derive asymptotics for the information-theoretic lower bound on the number of bits needed to store tree classes whose generating functions satisfy certain functional equations…