B+ tree is a data structure used to store (key, value) pairs in a tree-like structure for fast retrieval. It has a root node, intermediary nodes that point to leaf nodes but do not store data, and leaf nodes that store the actual records. Leaf nodes must contain a minimum and maximum number of values, and non-leaf nodes a minimum and maximum number of child nodes. B+ trees allow fast traversal and search via balanced structure and sorted nodes. Records are inserted and deleted by searching the tree to the appropriate leaf node and updating pointers and values.

1. B+ TREE
PRESENTED BY
M.RAMYA
Msc[CS&IT]
NADAR SARASWATHI COLLEGE OF ARTS &SCIENCE,
VADAPUDUPATTI , THENI.

2. INTRODUCTION
• B+ tree is a (key, value) storage method in a tree like structure.
B+ tree has one root, any number of intermediary nodes
(usually one) and a leaf node.
• Here all leaf nodes will have the actual records stored.
Intermediary nodes will have only pointers to the leaf nodes; it
not has any data.
• Any node will have only two leaves. This is the basic of any
B+ tree.

3. STRUCTURE OF B+ TREE
• A B+ tree index is a multilevel indexes , but it has a structure
that differs from than of the multilevel index-sequential file.
• The bucket structure is used only if the search key does not
from a primary key and if the file is not sorted in the search key
value in the order.

5. QUERIES ON B+ TREE
• Process queries using a b+ tree . To find all the records with a search-key
value of k.

6. • Leaf nodes must have between 2 and 4 values([(n-1)/2)] and n-
1 , with n=5).
• Non-leaf nodes other than root must have between 3 and 5
children([(n/2)]and n with n=5).
• Root must have at least 2 children.

7. UPADATES ON B+ TREES
INSERTION
If the search key value already appears in the leaf node , we add the new
record to the file and , if necessary , a pointer to the bucket.

8. DELETION
Using same technique as for lookup , we find the record to be deleted and
remove it from the file . The search key value is removed from the leaf
node if there is no bucket associated with that search key value or if the
bucket becomes empty as a result of the deletion.

9. B+TREE FILE ORGANIZATION
In a B+ tree file organization , the leaf nodes of the
tree store records instead of storing pointers to
records . An example of a B+ tree file organization .
Since records are usually larger than pointers , the
maximum number of records that can be stored in
the leaf nodes is less than the number of pointers in
a non leaf node.

11. MAIN GOAL OF B+ TREE IS:
• Sorted Intermediary and leaf nodes
Since it is a balanced tree, all nodes should be sorted.
• Fast traversal and Quick Search
Any record should be fetched very quickly. This is made by maintaining the
balance in the tree and keeping all the nodes at same distance
• No overflow pages
B+ tree allows all the intermediary and leaf nodes to be partially filled – it will have
some percentage defined while designing a B+ tree. In our example above,
intermediary node with 108 is underflow. And leaf nodes are not partially filled,
hence it is an overflow. In ideal B+ tree, it should not have overflow or underflow
except root node.