(a,b)-tree

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.

Definition

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 $\rho_v$ be the number of child nodes of node v.
• Let $S_v[1 \dots \rho_v]$ be pointers to child nodes.
• Let $H_v[1 \dots \rho_v - 1]$ be an array of keys such that $H_v[i]$ equals the largest key in the subtree pointed to by $S_v[i]$.

See also

• B-tree
• 2-3 tree
• 2-4 tree

References

• Black, Paul E. "(a,b)-tree". Dictionary of Algorithms and Data Structures. NIST.