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