Search results
Results from the WOW.Com Content Network
Depth only increases when the root is split, maintaining balance. Similarly, a B-tree is kept balanced after deletion by merging or redistributing keys among siblings to maintain the -key minimum for non-root nodes. A merger reduces the number of keys in the parent potentially forcing it to merge or redistribute keys with its siblings, and so on.
With the new operations, the implementation of weight-balanced trees can be more efficient and highly-parallelizable. [10] [11] Join: The function Join is on two weight-balanced trees t 1 and t 2 and a key k and will return a tree containing all elements in t 1, t 2 as well as k. It requires k to be greater than all keys in t 1 and smaller than ...
If the two trees are balanced, join simply creates a new node with left subtree t 1, root k and right subtree t 2. Suppose that t 1 is heavier (this "heavier" depends on the balancing scheme) than t 2 (the other case is symmetric). Join follows the right spine of t 1 until a node c which is balanced with t 2.
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.
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.
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 .
This partitioning method allows the tree to be traversed in ascending order if we travel the tree in in-order. This is why BATON supports range queries. To execute a range query q, BATON first locates its left bound, q.low. Then, the search process travels the tree in in-order (by adjacent link) until it reaches the upper bound, q.up.
Removing a point from a balanced k-d tree takes O(log n) time. Querying an axis-parallel range in a balanced k-d tree takes O(n 1−1/k +m) time, where m is the number of the reported points, and k the dimension of the k-d tree. Finding 1 nearest neighbour in a balanced k-d tree with randomly distributed points takes O(log n) time on average.