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For example, if binary tree sort is implemented with a self-balancing BST, we have a very simple-to-describe yet asymptotically optimal () sorting algorithm. Similarly, many algorithms in computational geometry exploit variations on self-balancing BSTs to solve problems such as the line segment intersection problem and the point location ...
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.
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.
In 2016, Blelloch et al. formally proposed the join-based algorithms, and formalized the join algorithm for four different balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps. In the same work they proved that Adams' algorithms on union, intersection and difference are work-optimal on all the four balancing schemes.
The AVL tree is named after its two Soviet inventors, Georgy Adelson-Velsky and Evgenii Landis, who published it in their 1962 paper "An algorithm for the organization of information". [2] It is the first self-balancing binary search tree data structure to be invented. [3]
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
The Day–Stout–Warren (DSW) algorithm is a method for efficiently balancing binary search trees – that is, decreasing their height to O(log n) nodes, where n is the total number of nodes. Unlike a self-balancing binary search tree , it does not do this incrementally during each operation, but periodically, so that its cost can be amortized ...
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height ... Fundamental Algorithms, Third Edition ...