Gap terminology and related combinatorial properties for AVL trees and Fibonacci-isomorphic trees

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

Two formalizations of AVL trees with room for extensions. The first formalization is monolithic and shorter, the second one in two stages, longer and a bit simpler. The final implementation is the same. If you are interested in developing this further, please contact .

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...

Adaptive Sorting with AVL Trees

A new adaptive sorting algorithm is introduced. The new implementation relies on using the traditional AVL trees, and has the same performance limitations. More precisely, the number of comparisons performed by our algorithm, on an input sequence of length n that has I inversions, is at most 1.44n lg I n + O(n) . Our algorithm runs in time O(n log I n ) and is practically efficient and easy to ...

Using AVL Trees for Fault Tolerant GroupKey