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A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n, but the cost of search, insert, and delete operations grows with the depth of the tree. As with any balanced tree, the cost grows much more slowly than the number of elements.
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
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Figure 1. Example of a Fibonacci heap. It has three trees of degrees 0, 1 and 3. Three vertices are marked (shown in blue). Therefore, the potential of the heap is 9 (3 trees + 2 × (3 marked-vertices)).
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.
A problem related to the order-maintenance problem is the list-labeling problem in which instead of the order(X, Y) operation the solution must maintain an assignment of labels from a universe of integers {,, …,} to the elements of the set such that X precedes Y in the total order if and only if X is assigned a lesser label than Y.
In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that can be used to implement dictionaries. The numbers mean a tree where every node with children (internal node) has either two, three, or four child nodes: a 2-node has one data element, and if internal has two child nodes;
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.