(a) Assume that the entire of relation R(A,B) fits in the available main memory but relation S(A,C) is too large to fit in the main memory. Find a fast join algorithm, i.e., an algorithm with the lowest number of I/O access, for the natural join of R and S. Justify that your proposed algorithm is the fastest possible join algorithm to compute the natural join of R and S. Next, assume that there is clustered index on attribute A of relation S. Explain whether or how this will change your answer. (1 point) (a) Assume that the entire of relation R(A,B) fits in the available main memory but relation S(A,C) is too large to fit in the main memory. Find a fast join algorithm, i.e., an algorithm with the lowest number of I/O access, for the natural join of R and S. Justify that your proposed algorithm is the fastest possible join algorithm to compute the natural join of R and S. Next, assume that there is clustered index on attribute A of relation S. Explain whether or how this will change your answer. (1 point)