A B+-tree index is to be built on the Name attribute of the STUDENT relation.…
2025
A B+-tree index is to be built on the Name attribute of the STUDENT relation. Each student name occupies 8 bytes, each disk block is 512 bytes, and each index pointer occupies 4 bytes. What is the best choice for the degree of the B+-tree, where degree means the maximum number of pointers in an internal node?
Answer: C. 43 — CONCEPTFor an internal B+-tree node of degree p, there are p child pointers and p − 1 search-key values. The largest feasible degree is the greatest integer p…
- A.
16
- B.
42
- C.
43
- D.
44
Attempted by 185 students.
Show answer & explanation
Correct answer: C
CONCEPT
For an internal B+-tree node of degree p, there are p child pointers and p − 1 search-key values.
The largest feasible degree is the greatest integer p for which the node’s total storage does not exceed one disk block.
APPLICATION
Let p be the number of pointers in an internal node.
Pointer storage is 4p bytes, while key storage is 8(p − 1) bytes.
Apply the block-size constraint: 4p + 8(p − 1) ≤ 512.
Simplify: 12p − 8 ≤ 512, so 12p ≤ 520 and p ≤ 43.33… .
Because p must be an integer, the largest possible degree is 43.
CROSS-CHECK
For p = 43, the node uses 43 × 4 + 42 × 8 = 508 bytes, which fits. For p = 44, it would use 44 × 4 + 43 × 8 = 520 bytes, which exceeds 512 bytes.
Therefore, the best choice is 43.