We have a shared$-$nothing system with $4$ processing nodes $($PNs$).$ The TIJ algorithm is used to join

two relations R and S$.$ R has $12,000$ pages and S has $8,000$ pages. The two relations are distributed

among the $4$ PNs$.$ PN$1$ has $40\%$ of the R and S tuples. PN$2,$ PN$3,$ and PN$4$ each have $20\%$ of the tuples.

$$ Hashing R and S results in bucket skew: The first $$ of the hash buckets together have $40\%$ of the

tuples. Each of the remaining three $$ has $20\%$ of the tuples.

$$ Each PN can only access one page from its disks at a time, i$.$e$.,$ no parallel I$/$O within each PN$.$

$$ Computation and communication times are negligible $($i$.$e$.,$ the analysis is based on I$/$O costs$).$

Assume that the joins of the bucket pairs do not encounter memory overflow $($i$.$e$.,$ at least one of the

operands fits in the memory$).$ Estimate the computation costs $($in terms of number of IOs$)$ for each

of the four phases using the following table. What is the total cost of this join operation.

Now Calculate Reading cost$($number of disk accesses$)$ and writing cost$($number of disk accesses$)$ Hashing, Partition Tuning and Bucket Tuning. What is the reading cost of Join?. Need to explain the calculation.

Hints:use Grace Algorithm calculation