---

How many keys to store in a B⁺-tree node

---

---

---

 

Slideshow:

Question: how many keys (and pointers) can you store in a B⁺-tree node ?

How many search keys (and pointers) can you store in 1 disk block ?
Computing the (maximum) number of keys in a B⁺-tree node

Computing the (maximum) number of keys in a B⁺-tree node

Computing the (maximum) number of keys in a B⁺-tree node

Example - Computing the (maximum) number of keys in a B⁺-tree node

❮ ❯



---

---

---

---

• Computing n:   the number of search keys (and pointers) in a node of the B⁺-tree
  • Fact:

    A node (both internal and external) of the B+-tree is stored in a disk block

    ---

    ---

  • Consequently:

    We will always pack a disk block with the maximum number of search keys !!!!

    ---

    ---

  • How to compute n (the number of search keys in a node):

    Let: Sk = length of a search key (in bytes) Sp = length of a pointer (in bytes) A FULL node contains: n search keys = n × Sk bytes n+1 pointers = (n+1) × Sp bytes Total number of bytes used: n × Sk + (n+1) × Sp How to find n: We must find the largest value of n such that n × Sk + (n+1) × Sp ≤ BlockSize

    Example:

    BlockSize = 4096 bytes Sk = 4 bytes (search key) Sp = 8 bytes Then: 4n + 8(n+1) ≤ 4096 12n + 8 ≤ 4096 12n ≤ 4088 n ≤ 340.666 ===> n = 340 search keys in 1 block