1. MTree An implementation and An example with m=3B C

2. Mtree (m=3) m = 3 a node contains at most 2 pieces of dataX A B C
m = 3
a node contains at most 2 pieces of data
an then branches 3 ways
a node contains at least one piece of data
and then branches 2 ways
it is a 2-3 tree
m = 4
a node contains at most 3 pieces of data
an then branches 4 ways
a node contains at least one piece of data
and then branches 2 ways
it is a 2-4 tree

3. Mtree (m=3) X A B C

4. X A B C

5. X A B C
NOTE:
we do not show parent link
m is the maximum branching factor

6. Mtree (m=3) X A B C
Another view

7. An example of an insertion leading to a split.
Split A X A B C
An example of an insertion leading to a split.
For m=3 there are 3 cases
Only one is presented

8. Insertion resulting in overflow
Split A X A B C
Insertion resulting in overflow

9. Split A X A B C
Create a new node A’ X A A’ B C

10. Split A Create a new node A’ insert largest element in A into A’ X A B

11. Split A Create a new node A’ insert largest element in A into A’X A B C
Create a new node A’
insert largest element in A into A’
remove that element from A X A A’ B C

12. Add/Insert largest element in A into X
Split A X A B C
Add/Insert largest element in A into X X A A’ B C

13. Add/Insert largest element in A into X
Split A X A B C
Add/Insert largest element in A into X
Remove that element from A X A A’ B C

14. Add/Insert largest element in A into X
Split A X A B C
Add/Insert largest element in A into X
Remove that element from A
Update pointer to A’ X A A’ B C

15. Add/Insert largest element in A into X
Split A X A B C
Add/Insert largest element in A into X
Remove that element from A
Update pointer to A’
Update pointer to A X A A’ B C

16. Split X X A B C
X now splits X A A’ B C

17. Split X
Another view X A A’ B C

18. We might also consider the cases when B splits when C splits m = 4 X A B C
We might also consider the cases
when B splits
when C splits
m = 4
m is large
deletion