Relaxed Balance through Standard Rotations

We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are un-coupled from updates, their total number is bounded by O(M log(M +N)), where M is the number of updates to an AVL tree of initial size N. Hence, relaxed balancing of AVL trees comes at no extra cost asymptotically. Furthermore , our scheme diiers from most other relaxed balancing schemes in an important aspect: No rebalancing transformation can be done in the wrong direction, i.e., no performed rotation can make the tree less balanced. Moreover, each performed rotation indeed corresponds to a real imbalance situation in the tree. Our results are important in designing eecient concurrency control strategies for main-memory databases. Main-memory search structures have gained new applications in large embedded systems, such as switching systems for mobile telephones.