Chapter 14, Problem 9PE

Explanation of Solution

a.

Losing sequentiality:

In B+ tree index or file organization, the leaf nodes loose sequentiality because of the following reasons:

• Here, even if the leaf nodes are adjoining each other in the tree, in the disk they may be located at different places...

Explanation of Solution

b.

i.

Worst-case occupancy:

• Simply rebuilding the indices can help to restore this sequentiality in the file organization.
• Consider the given alternative reorganization to restore this sequentiality.
• Here, every n-block unit and every B+ tree’s node are half filled.
• So, the worst-case occupancy will be 25%.

ii.

Allocating leaf nodes:

“No”, the given situation is not possible.

It is because of the following reasons:

• Consider the scenario when the n-block unit splits;
  • One n-block unit will contain the first “n/2” leaf pages.
  • The second n-block unit will contain the remaining leaf pages.
• So, each split in the n-block will preserve the order.
• As a result, the nodes in each n-block unit will always be successive.

iii.

Numbers of seeks required:

• First consider the case of a n-page block,
  • Here, while scanning the B+ tree, the leaf page might turn out to be non-sequential...