1. B-Trees B-trees are characterized in the following way:
they are search trees
they have large branching factors
they are good for organizing data on external media

2. B-Trees and Disk Drives - 1
Any node contains n[x] keys and n[x]+1 children
Branching factors are typically between
Height is very shallow minimizing disk accesses
The node size matches the sector size on the disk

3. B-Trees and Disk Drives - 2
Assume a branching factor of 1000
Only the root node is kept in memory
With one disk access over 1,000,000 keys are accessed; with two disk accesses over one billion keys can be accessed

4. B-Tree Definitions
Every node contains the number of keys (n[x]), the keys in nondecreasing order, and a boolean (leaf[x]) indicating whether a leaf or not
There are n[x]+1 pointers in internal nodes
The keys separate the ranges of keys in subtrees
Every leaf is at the same depth (height of the tree)
t (>= 2) is the minimum degree of the tree
every node (but the root) must have at least t-1 keys
every node has at most 2t-1 keys and 2t children

5. Height of a B-Tree
If n  1 for any n-key B-Tree of height h and minimum degree t  2 then