Data Structures and Algorithms, Week 08, Lecture 1 1
1 B-Trees, Definition
•Definition. Suppose mis a positive integer. Then a B-tree of order m
is a tree with the following properties.
1. Each nonempty node other than the root has between dm
2eand m
children.
2. If the tree is nonempty, the root has between 2 and mchildren.
3. If a node has cchildren then it stores c−1 keys in increasing
order.
4. If the keys stored in a node are
k1< k2<· · · < ks,
then
(a) all keys stored in leftmost or 0th subtree are less than k1,
(b) all keys stored in the ith subtree, 1 ≤i < s, lie between ki
and ki+1,
(c) and all keys stored in the last subtree are greater than than
ks.
5. All the leaves have the same depth.
