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A B+ tree or B plus tree is a type of tree which represents classified data in a way that allows for efficient insertion, retrieval and remotion of records, each of which is identified by a key. It is a dynamic, multilevel index, with maximum and minimum bounds on the number of keys in each index segment. In a B+ tree, all records are stored at the leaf level of the tree; only keys are stored in interior nodes.

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fig:B-Plus Tree

The primary value of a B+ player is in storing data for efficient retrieval in a block-oriented storage context-in particular, filesystems. This is primarily because unlike binary search tree, B+ trees have very high fanout, which reduces the number of I/O operations required to find an element in the tree.

B Plus Tree Index Files:

B+-tree indices are an alternative to indexed-sequential files.

  • A B+ index tree is a balanced tree in which every path from root to leaf is of equal length and each non leaf node has between ceiling(n/2) and n nodes where n is fixed.

  • B+ tree index structure is most widely used of various index structures that maintain their despite insertion and deletion of data.

Typical node is a B+ tree:

n-1 search keys K1, K2,… Kn-1

n pointers P1, P2, …Pn

  • Advantage of B+-tree index files: automatically reorganizes itself with small, topical, changes, in the face of insertions and deletions. Reorganization of entire file is not required to maintain performance.
  • Disadvantage of indexed-sequential files: performance degrades as file grows, since many overflow blocks get created. Periodic reorganization of entire file is required.

A B+-tree is a rooted tree satisfying the following properties:

  • All paths from root to leaf are of the same length
  • Each node that is not a root or a leaf has between [n/2] and n children.
  • A leaf node has between [(n–1)/2] and n–1 values

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