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Merge signature block justification

now how do we evaluate the cost of the sort merge join well we are going to sort r sort s and then we will scan r and s and merge them in memory so the cost is basically the cost of sorting r plus this cost of sorting s plus the cost of scanning r and s in the worst case actually all of the joint values of r and all of the joint values of s are exactly the same in that case the output is the cross product of all the tuples in r and s because everything matches so in that case it degenerates into a nested loop joint with cost of vertical bar r times bracket s which is actually lower than the cost of the sort merge joint but that's extremely unlikely and it's the kind of thing that a good optimizer would keep an eye out for and avoid so we can usually assume that in a sort merged joint there's plenty of distinct values in the joint columns and those little mini cross products where we take multiple join keys on r multiplied to the same joint key on s and we form all pairs that only happens on a handful of tuples like we saw in our example assuming that's the case and we don't pay extra ios for those little mini cross products of duplicates how big does the buffer have to be to do this in two passes each well suppose that the buffer is bigger than the square root of the larger of r and s so then both r and s can be sorted in two passes and given that we can now compute the cost of our algorithm on our inputs r is a thousand pages and we know that sorting is two passes of r so that's two read and write passes so that's four times one thousand sorting as again takes two read and write passes so that's four times five hundred and then the final pass to read our read s and merge them together in a streaming fashion and that's 1 000 plus 500 for a total of 7 500 ios for this sort merge join now in general figuring out the cost of the sorting the output of the joint is a bit tricky because we don't know how big the output of the joint will be it depends on how many matches we find between these two tables but in this particular example we happen to know that every reservation has exactly one sailor and so the output is going to be exactly the same number of rows as the input table are the number of reserves tuples so we can estimate the cost of sorting the output here as the cost of sorting r which you can see below and that's something like 4 000 ios for grand total with block nested loops join of 9500 ios to do...