Query Optimization $-$ Estimating I$/$O costs

Using two relations R and S $,$ with the join condition $\backslash (\backslash$mathrm$\{$Ri$\}=\backslash$mathrm$\{$Sj$\}\backslash ),$ and given the following information:

$-\backslash ($ M $\backslash )$ pages in $\backslash ($ R $\backslash )$ with $\backslash ($ p R $\backslash )$ tuples per page

$-\backslash ($ N $\backslash )$ pages in $\backslash ($ S $\backslash )$ with $\backslash ($ p S $\backslash )$ tuples per page

R contains:

$-500$ pages

$-20$ tuples per page

S contains:

$-800$ pages

$-40$ tuples per page

Buffer size is $52($inclusive of $2$ additional buffers$)$

$5.$ Compute the I$/$O cost for R JOIN S using a block nested loop join

$6.$ Compute the I$/$O cost for S JOIN R using a block nested loop join

$7.$ Compute the I$/$O cost for $\backslash ($ R $\backslash )$ and $\backslash ($ S $\backslash )$ using a hash join.

Show all your work.

The questions will not be graded without the work shown.

Using two relations $\backslash ($ S $\backslash )$ and $\backslash ($ R $\backslash ),$ suppose that $\backslash ($ S $\backslash )$ has $500$ tuples stored in $50$ disk blocks and $\backslash ($ R $\backslash )$ has $10,000$ tuples stored in $1,000$ disk blocks. The following information is provided for access paths:

$102$ buffer caches $($pages$)$ are available.

The relation S has the secondary Index on sID with index level $\backslash (=2\backslash )$ and the relation $\backslash ($ R $\backslash )$ has the secondary index on sID with index level $\backslash (=1\backslash )$

Each $\backslash ($ S $\backslash )$ tuple matches with exactly $\backslash (8$ R $\backslash )$ tuples.

$8.$ What is the IO costs for the join $\backslash ($ S $\backslash$bowtie R $\backslash )$ : S $.$sID $=$ R $.$sID using index based nested loop join? SJOIN R