Consider processing the following SQL projection query:

SELECT DISTINCT E.title, E.ename FROM Executives E

You are given the following information:

Executives has attributes ename, title, dname, and address; all are string fields of the same length.

The ename attribute is a candidate key.

The relation contains 10,000 pages.

There are 10 buffer pages.

Consider the optimized version of the sorting-based projection algorithm: The initial sorting pass reads the input relation and creates sorted runs of tuples containing only attributes ename and title. Subsequent merging passes eliminate duplicates while merging the initial runs to obtain a single sorted result (as opposed to doing a separate pass to eliminate duplicates from a sorted result containing duplicates).

1. How many sorted runs are produced in the first pass? What is the average length of these runs? (Assume that memory is utilized well and that any available optimization to increase run size is used.) What is the I/O cost of this sorting pass?

2. How many additional merge passes will be required to compute the final result of the projection query? What is the I/O cost of these additional passes?

3. (a) Suppose that a clustered B+ tree index on title is available. Is this index likely to offer a cheaper alternative to sorting? Would your answer change if the index were unclustered? Would your answer change if the index were a hash index?

(b) Suppose that a clustered B+ tree index on ename is available. Is this index likely to offer a cheaper alternative to sorting? Would your answer change if the index were unclustered? Would your answer change if the index were a hash index?

(c) Suppose that a clustered B+ tree index on hename, titlei is available. Is this index likely to offer a cheaper alternative to sorting? Would your answer change if the index were unclustered? Would your answer change if the index were a hash index?

4. Suppose that the query is as follows:
SELECT E.title, E.ename FROM Executives E
That is, you are not required to do duplicate elimination. How would your answers to the previous questions change?