TAOCP 6.2.4 Exercise 4

Section 6.2.4: Multiway Trees

Exercise 4. [21] [21] (Bayer and McCreight.) Explain how to handle insertions into a generalized B-tree so that all nodes except the root and leaves will be guaranteed to have at least 3

1 . zm, 5 children.

Verified: no
Solve time: 4m05s

Correct solution

We restart from the standard Bayer–McCreight B-tree model and make explicit the structural object being modified.

A B-tree of order $m$ is a rooted search tree in which each internal node $v$ stores:

• a sorted sequence of separator keys $k_1 < \dots < k_{t-1}$,
• $t$ child pointers $c_1,\dots,c_t$,
• with $t \le m$, and $t-1$ keys.

All leaves are at the same level. Subtrees satisfy the usual search ordering determined by separator keys.

We impose the