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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 Spring '13
 Dr.Khansari
 hash function, Prime number, Bucket address table

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