B-tree(Balanced Tree Index) is a self-balancing tree data structure. The B-tree is a generalization of a binary search and it is optimized by systems in-order to keep logarithmic time.
In B-trees, internal (non-leaf) nodes can have a variable number of child nodes within some pre-defined range. When data is inserted or removed from a node, its number of child nodes changes. In order to maintain the pre-defined range, internal nodes may be joined or split. Because a range of child nodes is permitted, B-trees do not need re-balancing as frequently as other self-balancing search trees but may waste some space, since nodes are not entirely full.
Each internal node of a B-tree contains a number of keys. The keys act as separation values which divide its subtrees. For example, if an internal node has 3 child nodes(or subtrees) then it must have 2 keys:
a2. All values in the leftmost subtree will be less than
a1, all values in the middle subtree will be between
a2, and all values in the rightmost subtree will be greater than
Usually, sorting and searching algorithms have been characterized by the number of comparison operations that must be performed using order notation. A binary search of a sorted table with N records, for example, can be done in roughly
o(log N). If the table had 1,000,000 records, then a specific record could be located with at most 20 comparisons:
log (1,000,000) = 20.
There are some advantages of B-tree usage for a database. A B-tree:
- keeps keys in sorted order for sequential traversing
- uses a hierarchical index to minimize the number of disk reads
- uses partially full blocks to speed insertions and deletions
- keeps the index balanced with a recursive algorithm
In addition, a B-tree minimizes waste by making sure the interior nodes are at least half full. A B-tree can handle an arbitrary number of insertions and deletions.
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