Amortized complexity of bulk updates in AVL-trees

Abstract

A bulk insertion for a given set of keys inserts all keys in the set into a leaf-oriented AVL-tree. Similarly, a bulk deletion deletes them all. The bulk insertion is simple if all keys fall in the same leaf position in the AVL-tree. We prove that simple bulk insertions and deletions of m keys have amortized complexity O(logm) for the tree adjustment phase. Our reasoning implies easy proofs for the amortized constant rebalancing cost of single insertions and deletions in AVL-trees. We prove that in general, the bulk operation composed of several simple ones of sizes m1,…, mk has amortized complexity O(Σki=1 log mi).