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ASSIGNMENT 4 – 601.315/415/615 – Databases

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ASSIGNMENT 4 – 601.315/415/615 – Databases

Questions

(1) Consider the following relational schema and SQL query (next page).
EMPLOYEE SSN Name DNO Salary Hobby Sex
339-18-4886 Milton Kent 520 65000 Golf M
DEPARTMENT DNO DName Budget Location MGRSSN
520 Accounting 10000000 NEB 339-18-4886
WORKS ON ESSN PNUM
339-18-4886 109
PROJECT PNUM PName Budget Location Goal
520 F16Engine 30000000 NEB Profit
Assume that there are 50,000 employees, 1,000 projects, 30 departments 50% of employees are male, 0.01% of employees have a yodeling hobby, the Relational Mechanics
department only has 6 members and the median project budget is $1,000,000. 5 people work on the F16Engine project.
(a) Convert the following SQL query into the relational algebra and draw a query
tree for it for the most efficient execution ordering you can think of.
SELECT E.LName
FROM Employee E, Department D, WorksON W, Project P
WHERE E.DNO=D.DNO and E.SSN=W.ESSN and P.PNUM=W.PNUM
and P.Budget > $50 and E.Sex=’M’ and E.hobby=’Yodeling’
and D.Dname=’Rational Mechanics’;
(b) Convert the following SQL query into the relational algebra and draw a query
tree for it for the most efficient execution ordering you can think of.
SELECT E.LName, D.DNO
FROM Employee E, Department D, WorksON W, Project P
WHERE E.DNO=D.DNO and E.SSN=W.ESSN and P.PNUM=W.PNUM
and P.Fname=’F16Engine’ and E.Sex=’M’
(2) Consider the following two transactions:
T0 T1
read item(A) read item(B)
read item(B) read item(A)
if A=0 then B :=B+1 if B=0 then A := A+1
write item(B) write item(A)
(a) Show a concurrent execution of T0 and T1 which produces a serializable schedule
(Represent concurrent executions as shown in the table in problem 7).
(b) Show a concurrent execution of T0 and T1 which produces a non-serializable
schedule
(3) Consider the following 3 transactions, consisting of a sequence of read and write
operations, with (omitted) intermediate code.
T0 T1 T2
read item(X) read item(Z) read item(Y)
write item(X) read item(Y) read item(Z)
read item(Y) write item(Y) write item(Y)
write item(Y) read item(X) write item(Z)
write item(X)
Now consider the following concurrent schedule of these 3 transactions. Is this schedule conflict serializable? Why or why not (create a labeled precedence graph to help
you argue). If it is conflict serializable, give an equivalent serial schedule.
(See table on the following page)
T0 T1 T2
read item(Z)
read item(Y)
write item(Y)
read item(Y)
read item(Z)
read item(X)
write item(X)
write item(Y)
write item(Z)
read item(X)
read item(Y)
write item(Y)
write item(X)
(4) Consider the 3 transactions given in problem 3, along with the following concurrent
schedule. Is this schedule conflict serializable? Why or why not (create a labeled
precedence graph to help you argue). If it is conflict serializable, give a equivalent
serial schedule.
T0 T1 T2
read item(Y)
read item(Z)
read item(X)
write item(X)
write item(Y)
write item(Z)
read item(Z)
read item(Y)
write item(Y)
read item(Y)
write item(Y)
read item(X)
write item(X)
(5) Consider the precedence graph below. Is the corresponding transaction history conflict serializable? If so, give an equivalent valid serial schedule for the transactions.
PLEASE SEE ATTACHMENT ON CLASS WEBSITE FOR DIAGRAM.
(6) Consider the labeled precedence graph below. Is the corresponding transaction history
conflict serializable? If so, give an equivalent valid serial schedule for the transactions.
PLEASE SEE ATTACHMENT ON CLASS WEBSITE FOR DIAGRAM.
(7) Consider a relation that is fragmented horizontally by PlantLocation:
EMPLOYEE Name Title Salary PlantLocation
Joe Steel Foreman 65000 Edmonton
Assume each fragment has two replicas: one stored at the New York office and one
stored locally at each plant location. Describe a good processing strategy for the
following queries entered at the San Jose plant location.
(a) Find all employees at the ’Boca’ plant.
(b) Find the average salary of all employees in the company.
(c) Find the highest-paid employee at each of the following locations Toronto, Edmonton, Vancouver, Montreal.
(c) Find the lowest paid employee in the entire company.
(8) Consider the relations:
EMPLOYEE Name Title Salary PlantLocation
Joe Steel Foreman 65000 Edmonton
MACHINE MachineNumber Type PlantLocation
117 Infusinator Edmonton
Assume the EMPLOYEE relation is fragmented horizontally by PlantLocation and
each fragment is store locally at its corresponding plant site. Assume the MACHINE
relation is stored in its entirty at the Armonk site. Describe a good strategy for
processing each of the following queries.
(a) Find all employees at the plant containing machine number 1130.
(b) Find all employees at plants containing machines whose type is “Milling Machine”
(c) Find all machines at the Almaden plant.
(c) Compute EMPLOYEE ✶ MACHINE.
(9) Compute r ✶ s and s semijoin r for the following relations:
r:
A B C
9 1 8
2 3 5
6 4 3
5 6 7
2 3 4
s:
C D E
4 5 6
3 4 3
1 3 4
1 5 2
4 7 9
(10) If a hash structure is used on a search key for which range queries are likely, what
property should the hash function have?
(11) Recall that the hash join algorithm (for the natural inner join A ✶ B) basically adds
the join attribute of B to the hash table, then hashes on A into the same table. If a
match is found, then the join on that attribute succeeds. If no match is found, the
join on that attribute does not succeed, but the attribute of A is not added to the
hash table.
Briefly list the changes necessary to this algorithm for to handle a full outer join.
(12) Suppose that the bank used in the textbook’s running example maintains a statistical database containing the average balances of all customers. The scheme for this
relation is (customer-name, customer-city, avg-balance). Assume that for security
reasons, the following restrictions are imposed on queries against this data:
• Every query must involve at least 10 customers
• The intersection of any pair of queries must be at most 5.
Construct a series of queries to find the average balance of a customer. (Hint: this
can be done in fewer than 7 queries.)
(13) Suppose that we decompose the schema r(A,B,C,D,E) into r1(A,B,C) and r2(A,D,E).
Show that this decomposition is a lossless decomposition if the following set F of
functional dependencies holds:
A → BC
CD → E
B → D
E → A
(14) Compute the closure of the set of functional dependencies from problem 13.
(15) Compute the canonical cover Fc of the set of functional dependencies from problem
13.
(16) Compute B+ given the set of functional dependencies from problem 13.
(17) Use Armstrongs’s axioms to prove the soundness of the pseudotransitivity rule.
(18) Given the databse schema R(a, b, c), and a relation r on the schema R, write a SQL
query to test whether the funciontal dpendency b → c holds on relation r. There is
no need to deploy/test this SQL code.
(19) Write a SQL assertion that enforces the functional dependency from Question 17;
assume that no null values are present. There is no need to deploy/test this SQL
code.
(20) Show that the decomposition in problem 13 is not a dependency preserving decomposition.
(21) Give an example of a relational schema R0 and the set F
0 of functional dependencies
such that there are at least three distinct lossless decompositions of R0
into BCNF.

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