Question

In a B+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases?

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2024 answer key

Solution

Recall the B+ tree node occupancy invariant for the root node versus internal and leaf nodes.

In a B+ tree of order mm, every non-root internal node and every non-root leaf node must remain at least half full (⌈m/2⌉\lceil m/2 \rceil children or ⌈(m−1)/2⌉\lceil (m-1)/2 \rceil keys) to guarantee logarithmic height. This 50%50\% minimum occupancy requirement is relaxed only for the root node, which is allowed to have as few as 11 search key (22 child pointers) when it is not a leaf.

Final answer

Option (A)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2024 Computer Science and Information Technology - Set 1 (CS1)
Question
21 of 65
Section
Computer Science and Information Technology

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