Question:

(a) The objective of query optimization is to choose the most efficient strategy for implementing a given relational query, thereby improving the system performance. One of the stages of query optimization is to convert the internal form into equivalent and more efficient canonical form, using well-defined transformation rules. Two rules of the transformation rules is given below:

Rule 1 - Transform a sequence of restrictions against a given relation into a single (ANDed) restriction.

Rule 2 - Transform a restriction of a projection into a projection of a restriction.

(i) Explain what is meant by each of the above rules.

(ii) Using the relational schema given in Appendix, provide example of each of the above rules.

(b) Refer to the relational schema given in Appendix.

Assuming that:

 The Employee relation contains 1000 records among which 300 employee are assigned to departments located in the United States.
- The Department relation contains 30 records among which 20 departments are located in United States
- The Location relation contains 20 records among which 5 are situated in the United States.

(i) Express the following query in SQL:

"find the employee Last names and the department names who are working in United States (Location.country_id = US)

(ii) Choose two possible methods to evaluate the query, and use the relational algebra to formulate clearly all the steps required in the evaluation. For each method, calculate the number of tuples for all the intermediate relations (namely, size of the intermediate relations) required for each step.