The purpose of the IAVL+ data structure is to provide persistent storage for key-value pairs in the application state such that a deterministic Merkle root hash can be computed efficiently. The tree is balanced using a variant of the AVL algorithm, and all operations are O(log(n)).
In an AVL tree, the heights of the two child subtrees of any node differ by at most one. Whenever this condition is violated upon an update, the tree is rebalanced by creating O(log(n)) new nodes that point to unmodified nodes of the old tree. In the original AVL algorithm, inner nodes can also hold key-value pairs. The AVL+ algorithm (note the plus) modifies the AVL algorithm to keep all values on leaf nodes, while only using branch-nodes to store keys. This simplifies the algorithm while keeping the merkle hash trail short.
The AVL+ Tree is analogous to Ethereum’s Patricia tries. There are tradeoffs. Keys do not need to be hashed prior to insertion in IAVL+ trees, so this provides faster ordered iteration in the key space which may benefit some applications. The logic is simpler to implement, requiring only two types of nodes – inner nodes and leaf nodes. The Merkle proof is on average shorter, being a balanced binary tree. On the other hand, the Merkle root of an IAVL+ tree depends on the order of updates.