Consider the following BCNF relation, which lists the ids, types (e.g., nuts or bolts), and costs of various parts, along with the number that are available or in stock:

You are told that the following two queries are extremely important:

? Find the total number available by part type, for all types. (That is, the sum of the num avail value of all nuts, the sum of the num avail value of all bolts, etc.)

? List the pids of parts with the highest cost.

1. Describe the physical design that you would choose for this relation. That is, what kind of a file structure would you choose for the set of Parts records, and what indexes would you create?

2. Suppose that your customers subsequently complain that performance is still not satisfactory (given the indexes and file organization that you chose for the Parts relation in response to the previous question). Since you cannot afford to buy new hardware or software, you have to consider a schema redesign. Explain how you would try to obtain better performance by describing the schema for the relation(s) that you would use and your choice of file organizations and indexes on these relations.

3. How would your answers to the above two questions change, if at all, if your system did not support indexes with multiple-attribute search keys?