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Problem 1. (20 points) Consider a database buffer manager that uses the algorithm explained in

Section 13.5.1 of the textbook for a hard drive which takes 10 milliseconds per disk seek and can read 80MB per second.
(a) (10 points) Assume that (i) the size of each disk block is 8KB, (ii) the probability that thebuffer manager can handle a data request without accessing the disk (i.e., the probability that a requested block is already in the buffer) is 90%, (iii) only 10% of disk block accesses require a disk seek (i.e., 90% of the disk blocks are read consecutively without requring any disk seek), (iv) no disk blocks are updated (i.e., no need to write dirty blocks back to the hard drive), and (v) the time spent for reading/writing data in the main memory is negligible (considered 0 milliseconds). Under these assumptions, calculate the expected data access time (i.e., how much time it would on average take to obtain a disk block from the buffer manager).
(b) (10 points) In contrast to the above scenario, assume that (i) the size of each disk block is 16KB,(ii) the probability that the buffer manager can handle a data request without accessing the disk (i.e., the probability that a requested block is already in the buffer) is 70%, and (iii) only 5% of disk block accesses require a disk seek (i.e., 95% of the disk blocks are read consecutively without requring any disk seek). Calculate the expected data access time as in (a). Also, based on the above calculations, explain whether it is more advantageous to use 8KB disk blocks or 16KB disk blocks.
Problem 2. (40 points) Consider the following relational database:

branch(branch_name , branch_city) customer(customer_number , customer_name , customer_city) loan(loan_number , branch_name , amount) borrower(customer_number , loan_number)
(b) (10 points) Using the schema of the customer relation, provide an example of a superkey which is not a candidate key. Explain why your answer is correct.
(c) (10 points) Given your choice of primary keys, identify all of the foreign keys. For each foreignkey, specify the referencing and referenced relations.
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(d) (10 points) For one of the foreign keys identified above, explain a situation where deleting a
record/tuple causes a violation of the foreign key constraint (referential integrity constraint).
Problem 3. (50 points) Answer the following problems. For each problem, start with the

B+-tree in Figure 1.

Figure 1: B+-Tree Example
(c) (10 points) Draw the tree that would result from deleting 39 from the tree in Figure 1. Youmay omit the parts of the tree that do not change.

After solving the above problems, please state the amount of time spent for this assignment. Feel free to add comments or suggestions if any.
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