Assume we have a Shared Nothing System with $4$ processing nodes and we want to implement a GRACE algorithm & ABJ algorithm with the following:

R $$ S where R has $4,000$ pages and S has $8,000$ pages. Each relation is evenly divided among the four PNs$.$ Thus, each PN has $3,000$ pages of tuples. The Hashing Phase results in data skew as follows:

$1)30\%$ of the data in the first $8$ bucket pairs: R$0/$S$0-$ R$7/$S$7$

$2)20\%$ of the data in the second $8$ bucket pairs: R$8/$S$8$ R$15/$S$15$

$3)10\%$ of the data in the third $8$ bucket pairs: R$16/$S$16$ R$23/$S$23$

$4)10\%$ of the data in the fourth $8$ bucket pairs: R$24/$S$24$ R$31/$S$31$

Calculate the read cost, write cost, and total computation cost for BOTH algorithms. Please explain thoroughly. Please note that the computation cost for the Hash Phase of the Grace Algorithm is determined by the slowest processing node $($last to finish its workload$),$ not the sum of the local computation costs of all the processing nodes. I need to understand the main difference for both algorithms.Assume we have a Shared Nothing System with $4$ processing nodes and we want to implement a GRACE algorithm & ABJ algorithm with the following:

R $$ S where R has $4,000$ pages and S has $8,000$ pages. Each relation is evenly divided among the four PNs$.$ Thus, each PN has $3,000$ pages of tuples. The Hashing Phase results in data skew as follows:

$1)30\%$ of the data in the first $8$ bucket pairs: R$0/$S$0-$ R$7/$S$7$

$2)20\%$ of the data in the second $8$ bucket pairs: R$8/$S$8$ R$15/$S$15$

$3)10\%$ of the data in the third $8$ bucket pairs: R$16/$S$16$ R$23/$S$23$

$4)10\%$ of the data in the fourth $8$ bucket pairs: R$24/$S$24$ R$31/$S$31$

Calculate the read cost, write cost, and total computation cost for BOTH algorithms. Please explain thoroughly. Please note that the computation cost for the Hash Phase of the Grace Algorithm is determined by the slowest processing node $($last to finish its workload$),$ not the sum of the local computation costs of all the processing nodes. I need to understand the main difference for both algorithms.