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  2. B-tree - Wikipedia

    en.wikipedia.org/wiki/B-tree

    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 ...

  3. 2–3–4 tree - Wikipedia

    en.wikipedia.org/wiki/2–3–4_tree

    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;

  4. B+ tree - Wikipedia

    en.wikipedia.org/wiki/B+_tree

    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.

  5. Order statistic tree - Wikipedia

    en.wikipedia.org/wiki/Order_statistic_tree

    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

  6. Fibonacci heap - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_heap

    Figure 2. First phase of delete-min. Figure 3. Third phase of delete-min. The delete-min operation does most of the work in restoring the structure of the heap. It has three phases: The root containing the minimum element is removed, and each of its children becomes a new root.

  7. Lazy deletion - Wikipedia

    en.wikipedia.org/wiki/Lazy_deletion

    [1] The problem with this scheme is that as the number of delete/insert operations increases, the cost of a successful search increases. To improve this, when an element is searched and found in the table, the element is relocated to the first location marked for deletion that was probed during the search.

  8. Treap - Wikipedia

    en.wikipedia.org/wiki/Treap

    When a key x is to be inserted into a tree that already has n nodes, the insertion algorithm chooses with probability 1/(n + 1) to place x as the new root of the tree, and otherwise, it calls the insertion procedure recursively to insert x within the left or right subtree (depending on whether its key is less than or greater than the root). The ...

  9. K-D-B-tree - Wikipedia

    en.wikipedia.org/wiki/K-D-B-tree

    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.