(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 $2 \leq a \leq (b +1)/2$ . The root has, if it is not a leaf, between 2 and $b$ children.

Definition

Let $a$ , $b$ be positive integers such that $2 \leq a \leq (b +1)/2$ . 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

Every internal node $v$ of a (a,b)-tree $T$ 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 $S_{v}[i]$ .