AVL Trees

0 Rank - Balanced Trees

Since the invention of AVL trees in 1962, many kinds of binary search trees have been proposed. Notable are red-black trees, in which bottom-up rebalancing after an insertion or deletion takes O(1) amortized time and O(1) rotations worst-case. But the design space of balanced trees has not been fully explored. We continue the exploration. Our contributions are three. We systematically study the...

New Combinatorial Properties and Algorithms for AVL Trees

In this thesis, new properties of AVL trees and a new partitioning of binary search trees named core partitioning scheme are discussed, this scheme is applied to three binary search trees namely AVL trees, weight-balanced trees, and plain binary search trees. We introduce the core partitioning scheme, which maintains a balanced search tree as a dynamic collection of complete balanced binary tre...

AVL Trees with Relaxed Balance

The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in main-memory databases. In this paper, we describe a relaxed version of AVL trees. We prove that each update gives rise to at most a logarithmic number of rebalancing operations and that the number of rebalancing operations in the semidynamic case is amortized c...

Parallel Dictionaries with Local Rules on AVL and Brother Trees

We present a set of local rules to deal with dictionaries Their main advantage is that they can be scheduled in a highly synchronized way to get parallel dictionaries on AVL trees Up to now trees used in massively parallel dictionaries needed to have all the leaves at the same depth such as trees Therefore it was possible in insertions and deletions the bottom up reconstruction of the tree in a...

Using AVL Trees for Fault Tolerant GroupKey