We have a shared$-$nothing system with four processing nodes $($PNs$).$ The ABJ algorithm is used to join two relations R and S as discussed in class, each stored in $10,000$ pages. We make the following assumptions:

$$ We have initial data skew: PN$1$ has $30\%$ of the R and S tuples. PN$2,$ PN$3,$ and PN$4$ evenly have the remaining tuples $($i$.$e$.,$ approximately $23\mathrm{.}3\%$ each$).$

$$ Parallel read or write is not possible within a PN$.$

$$ Hashing results in data skew: The first $14$ of the hash buckets has $50\%$ of the data.

$$ Read or write a page takes D time units.

$$ Computation and communication times are negligible.