Do we mean different things by "merge join" and "nested loop join" ? For me "merge join" is O(n) (but requires the data to be sorted by key) whereas "nested loop join" is O(n^2).
Yes, if the data is not already sorted. Thus it's O(n) for already sorted data and O(n log(n) + n) -- which simplifies to O(n log(n)) -- for arbitrary data.
