B-tree, Data Structure & Algorithms

Unlike a binary-tree, each node of a B-tree may have a number of keys and children. The keys are stored or saved in non-decreasing order. Each key has an related child that is the root of a subtree containing all nodes with keys less than or equal to the key but greater than the preceding key. A node also contains an additional rightmost child that is the root for a subtree containing all keys greater than any keys in the node.

A B-tree has a minimum number of permissible children for each node known as the minimization factor. If t is this minimization factor, then every node must have at least t - 1 keys. Under certain conditions, the root node is allowed to violate this property by having fewer than t - 1 keys. Every node can have at most 2t - 1 keys or, equivalently, 2t children.

For n greater than or equal to one, the height of an n-key b-tree T of height h with a smallest degree t greater than or equal to 2, h≤logt (n+1/2)

 

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