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English: Analysis of data structures, tree compared to hash and array based structures, height balanced tree compared to more perfectly balanced trees, a simple height balanced tree class with test code, comparable statistics for tree performance, statistics of worst case strictly-AVL-balanced trees versus perfect full binary trees.
A node is α-weight-balanced if weight[n.left] ≥ α·weight[n] and weight[n.right] ≥ α·weight[n]. [7] Here, α is a numerical parameter to be determined when implementing weight balanced trees. Larger values of α produce "more balanced" trees, but not all values of α are appropriate; Nievergelt and Reingold proved that
A skip list does not provide the same absolute worst-case performance guarantees as more traditional balanced tree data structures, because it is always possible (though with very low probability [5]) that the coin-flips used to build the skip list will produce a badly balanced structure. However, they work well in practice, and the randomized ...
A binary tree is a rooted tree that is also an ordered tree (a.k.a. plane tree) in which every node has at most two children. A rooted tree naturally imparts a notion of levels (distance from the root); thus, for every node, a notion of children may be defined as the nodes connected to it a level below.
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, [1] is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.
Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items. Self-balancing binary search trees provide efficient implementations for mutable ordered lists , and can be used for other abstract data structures such as associative arrays , priority queues and sets .
For lookup-intensive applications, AVL trees are faster than red–black trees because they are more strictly balanced. [4] Similar to red–black trees, AVL trees are height-balanced. Both are, in general, neither weight-balanced nor μ {\displaystyle \mu } -balanced for any μ ≤ 1 2 {\displaystyle \mu \leq {\tfrac {1}{2}}} ; [ 5 ] that is ...
The BAlanced Tree Overlay Network (BATON) is a distributed tree structure designed for peer-to-peer (P2P) systems. Unlike other overlays that employ a distributed hash table, BATON organises peers in a distributed tree to facilitate range search.