---

Internal nodes of a B⁺-tree

---

---

---

 

Slideshow:

Structural requirements of B⁺-tree nodes

There are structural requirements and occupancy constraints on the internal nodes and the leaf nodes
Structure of an internal node
 
Occupancy constraint of an internal node

Occupancy constraint of an internal node
 
Occupancy constraint of an internal node
   
Occupancy constraint of an internal node
   
Occupancy constraint of an internal node
 
Summary+examples: structure and occupancy constraints on internal node

❮ ❯



---

---

---

---

• Structure of an internal node of a B⁺-tree
  • Structure of an internal node (including the root node):

    Explanation:

    Each internal node of the B+-tree is stored inside 1 disk block Search keys in a node are the search values that you want to use to speed up the search operation The pointers in the B+-node are database addresses to blocks that contains (another) node of the B+-node Property: There is 1 more pointer than search keys in a node I.e.: if there are k search keys then there are k+1 pointers in a node

  ---

  ---

  ---

  ---

• Occupancy constraint of an internal node of a B⁺-tree
  • Occupancy constraint on an internal node:

    At least half of the pointers in an internal node must be used

    Example:

    Suppose that a internal node can store: n       keys            and n+1   pointers (= database addresses) to other B+-tree nodes A full internal node is as follows: Each internal node must contain   ≥   ⌈ (n+1)/2 ⌉ pointers A minimal internal node:

  ---

  ---

  ---

  ---

• Exception to the occupancy constraint
  • Exception: the occupance constraint is not applicable to the root node of the B⁺-tree

    The root node must have at least 2 pointers (and 1 search key):

  ---

  ---

  ---

• Summary: (and a concrete examples with n = 3 and n = 4)

  Count the number of pointers in each node.
  At least half of the pointers must be used !!!