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To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
The B * tree balances more neighboring internal nodes to keep the internal nodes more densely packed. [2] This variant ensures non-root nodes are at least 2/3 full instead of 1/2. [13] As the most costly part of operation of inserting the node in B-tree is splitting the node, B *-trees are created to postpone splitting operation as long as they ...
If a large proportion of the elements of the tree are deleted, then the tree will become much larger than the current size of the stored elements, and the performance of other operations will be adversely affected by the deleted elements. When this is undesirable, the following algorithm can be followed to remove a value from the 2–3–4 tree:
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees.It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap.
A B+ tree consists of a root, internal nodes and leaves. [1] The root may be either a leaf or a node with two or more children. A B+ tree can be viewed as a B-tree in which each node contains only keys (not key–value pairs), and to which an additional level is added at the bottom with linked leaves.
Throughout insertion/deletion operations, the K-D-B-tree maintains a certain set of properties: The graph is a multi-way tree. Region pages always point to child pages, and can not be empty. Point pages are the leaf nodes of the tree. Like a B-tree, the path length to the leaves of the tree is the same for all queries.
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This is a fundamental requirement for the data-structure algorithms on B-tree to work. In particular then, a 2-3 tree is not a B-tree; it's algorithms are different than those of B-trees. The text currently uses 2-3 trees as a recurring example; those examples should be changed to refer to the 2-3-4-tree, the smallest example of a B-tree.