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In computer science, an (a,b) tree is a kind of balanced search tree.

An (a,b)-tree has all of its leaves at the same depth, and all internal nodes except for the root have between a and b children, where a and b are integers such that 2 ≤ a ≤ (b+1)/2. The root has, if it is not a leaf, between 2 and b children.


Let a, b be positive integers such that 2 ≤ a ≤ (b+1)/2. Then a rooted tree T is an (a,b)-tree when:

  • Every inner node except the root has at least a and at most b children.
  • The root has at most b children.
  • All paths from the root to the leaves are of the same length.

Internal node representation[edit]

Every internal node v of a (a,b)-tree T has the following representation:

  • Let be the number of child nodes of node v.
  • Let be pointers to child nodes.
  • Let be an array of keys such that equals the largest key in the subtree pointed to by .

See also[edit]


  •  This article incorporates public domain material from the NIST document: Black, Paul E. "(a,b)-tree". Dictionary of Algorithms and Data Structures.