# On the tree sequentiality is increasingly lost and

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on the tree, sequentiality is increasingly lost, and sequential access has to wait for disk seeks increasingly often. a. One way to solve this problem is to rebuild the index to restore sequentiality. b. i. In the worst case each n -block unit and each node of the B + -tree is half filled. This gives the worst case occupancy as 25 percent. ii. No. While splitting the n -block unit the first n / 2 leaf pages are placed in one n -block unit, and the remaining in the second n - block unit. That is, every n -block split maintains the order. Hence, the nodes in the n -block units are consecutive. iii. In the regular B + -tree construction, the leaf pages might not be sequential and hence in the worst case, it takes one seek per leaf page. Using the block at a time method, for each n -node block, we will have at least n / 2 leaf nodes in it. Each n -node block can be read using one seek. Hence the worst case seeks comes down by a factor of n / 2. iv. Allowing redistribution among the nodes of the same block, does not require additional seeks, where as, in regular B + -tree we require as many seeks as the number of leaf pages involved in the redistribution. This makes redistribution for leaf blocks efficient with this scheme. Also the worst case occupancy comes back to nearly 50 percent. (Splitting of leaf nodes is preferred when the participating leaf nodes are nearly full. Hence nearly 50 percent instead of exact 50 percent)
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