Rebalancing operations for deletions in AVL-trees

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...

Using AVL Trees for Fault Tolerant GroupKey

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 ...

Amortized Rotation Cost in AVL Trees

An AVL tree [1] is the original type of balanced binary search tree. An insertion in an n-node AVL tree takes at most two rotations, but a deletion in an n-node AVL tree can take Θ(log n). A natural question is whether deletions can take many rotations not only in the worst case but in the amortized case as well. A sequence of n successive deletions in an n-node tree takes O(n) rotations [3], b...