Polynormal subgroup

In computer science, an (a,b) tree is a specific kind of 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 $2\le a\le (b+1)/2$. The root has, if it is not a leaf, between 2 and b children.

Definition

Let $a,b\in \mathbb{\mathbb{N}}$ such that $a\le b$. Then a tree T is an (a,b) tree when:

• Every inner node except the root has at least $a$ and maximally $b$ child nodes.
• Root has maximally $b$ child nodes.
• 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

References

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