In computer science a T-tree is a type of binary tree data structure that is used by main-memory databases, such as Datablitz, eXtremeDB, MySQL Cluster, Oracle TimesTen and MobileLite.
A T-tree is a balanced index tree data structure optimized for cases
where both the index and the actual data are fully kept in memory, just as a B-tree is an index structure optimized for storage on block oriented secondary storage devices like hard disks. T-trees seek to gain the performance benefits of in-memory tree structures such as AVL trees while avoiding the large storage space overhead which is common to them.
T-trees do not keep copies of the indexed data fields within the index tree nodes themselves. Instead, they take advantage of the fact that the actual data is always in main memory together with the index so that they just contain pointers to the actual data fields.
The 'T' in T-tree refers to the shape of the node data structures in the original paper which first described this type of index.
A T-tree node usually consists of pointers to the parent node, the left and right child node, an ordered array of data pointers and some extra control data. Nodes with two subtrees are called internal nodes, nodes without subtrees are called leaf nodes and nodes with only one subtree are named half-leaf nodes. A node is called the bounding node for a value if the value is between the node's current minimum and maximum value, inclusively.
For each internal node, leaf or half leaf nodes exist that contain the predecessor of its smallest data value (called the greatest lower bound) and one that contains the successor of its largest data value (called the least upper bound). Leaf and half-leaf nodes can contain any number of data elements from one to the maximum size of the data array. Internal nodes keep their occupancy between predefined minimum and maximum numbers of elements
Search starts at the root node
If the current node is the bounding node for the search value then search its data array. Search fails if the value is not found in the data array.
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Un arbre splay (ou arbre évasé) est un arbre binaire de recherche auto-équilibré possédant en outre la propriété que les éléments auxquels on a récemment accédé (pour les ajouter, les regarder ou les supprimer) sont rapidement accessibles. Ils disposent ainsi d'une complexité amortie en O(log n) pour les opérations courantes comme insertion, recherche ou suppression. Ainsi dans le cas où les opérations possèdent une certaine structure, ces arbres constituent des bases de données ayant de bonnes performances, et ceci reste vrai même si cette structure est a priori inconnue.
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In computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing".
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