# Assignment 5 Object-relational databases Nested relational and semi-structured databases (Draft) solved

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For this assignment, you will need the material covered in the lectures
• Lecture 13: Object-relational databases and queries
• Lecture 14: Nested relational and semi-structured databases
To turn in your assignment, you will need to upload to Canvas a single file with name assignment5.sql which contains the necessary SQL statements that solve the problems in this assignment. The assignment5.sql file
must be so that the AI’s can run it in their PostgreSQL environment. You
should use the Assignment-Script-2021-Fall-assignment5.sql file to construct the assignment5.sql file. (Note that the data to be used for this assignment is included in this file.) In addition, you will need to upload a separate
assignment5.txt file that contains the results of running your queries. You
will also see several problems that are listed as practice problems. You should
not include your solutions for practice problems in the materials you submit for
this assignment.
1
1 Formulating Query in Object-Relational SQL
For the problems in the section, you will need to use the polymorphically defined
functions and predicates that are defined in the document
SetOperationsAndPredicates.sql
Functions
set union(A,B) A ∪ B
set intersection(A,B) A ∩ B
set difference(A,B) A − B
remove element(x,A) A − {x}
make singleton(x) {x}
choose element(A) choose some element from A
bag union(A,B) the bag union of A and B
bag to set(A) coerce the bag A to the corresponding set
Predicates
is in(x,A) x ∈ A
is not in(x,A) x 6∈ A
is empty(A) A = ∅
is not emptyset(A) A 6= ∅
subset(A,B) A ⊆ B
superset(A,B) A ⊇ B
equal(A,B) A = B
overlap(A,B) A ∩ B 6= ∅
disjoint(A,B) A ∩ B = ∅
We now turn to the problems in this section. You will need use the data
provided for the Person, Company, companyLocation, worksFor, jobSkill,
personSkill, and Knows relations. But before turning to the problems, we will
introduce various object-relational views defined over these relations:1
• The view companyHasEmployees(cname,employees) which associates with
each company, identified by a cname, the set of pids of persons who work
for that company.
create or replace view companyHasEmployees as
select cname, array(select pid
from worksfor w
where w.cname = c.cname order by 1) as employees
from company c order by 1;
1The various order by clauses in these views are not essential: they simply aid to read the
data more easily.
2
• The view cityHasCompanies(city,companies) which associates with each
city the set of cnames of companies that are located in that city.
create or replace view cityHasCompanies as
select city, array_agg(cname order by 1) as companies
from companyLocation
group by city order by 1;
• The view companyHasLocations(cname,locations) which associates with
each company, identified by a cname, the set of cities in which that company is located.
create or replace view companyHasLocations as
select cname, array(select city
from companyLocation cc
where c.cname = cc.cname order by 1) as locations
from company c order by 1;
• The view knowsPersons(pid,persons) which associates with each person, identified by a pid, the set of pids of persons he or she knows.
create or replace view knowsPersons as
select p.pid, array(select k.pid2
from knows k
where k.pid1 = p.pid order by pid2) as persons
from person p order by 1;
• The view isKnownByPersons(pid,persons) which associates with each
person, identified by a pid, the set of pids of persons who know that person.
Observe that there may be persons who are not known by any one.
create or replace view isKnownByPersons as
select distinct p.pid, array(select k.pid1
from knows k
where k.pid2 = p.pid) as persons
from person p order by 1;
• The view personHasSkills(pid,skills) which associates with each person, identified by a pid, his or her set of job skills.
create or replace view personHasSkills as
select distinct p.pid, array(select s.skill
from personSkill s
where s.pid = p.pid order by 1) as skills
from person p order by 1;
3
• The view skillOfPersons(skills,persons) which associates with each
job skill the set of pids of persons who have that job skill.
create or replace view skillOfPersons as
select js.skill, array(select ps.pid
from personSkill ps
where ps.skill = js.skill order by pid) as persons
from jobSkill js order by skill;
In the problems in this section, you are asked to formulate queries in objectrelational SQL. You should use the set operations and set predicates defined in
the document SetOperationsAndPredicates.sql, the relations
Person
Company
Skill
worksFor
and the views
companyHasEmployees
cityHasCompanies
companyHasLocations
knowsPersons
isKnownByPersons
personHasSkills
skillOfPersons
However, you are not permitted to use the Knows, companyLocation, and
personSkill relations in the object-relation SQL formulation of the queries.
Observe that you actually don’t need these relations since they are encapsulated
in these views.
Before listing the queries that you are asked to formulate, we present some
examples of queries that are formulated in object-relational SQL using the assumptions stated in the previous paragraph. Your solutions need to be in the
style of these examples. The goals is to maximize the utilization of the functions
and predicates defined in document SetOperationsAndPredicates.sql.
Example 1 Consider the query “ Find the pid of each person who knows a
person who has a salary greater than 55000.”2
select distinct pk.pid
from knowsPersons pk, worksfor w
where is in(w.pid, pk.persons) and w.salary > 55000
order by 1;
Note that the following formulation for this query is not allowed since it uses
the relation Knows which is not permitted.
2
In this example, focus on the is in predicate.
4
select distinct k.pid1
from knows k, worksfor w
where k.pid2 = w.pid and w.salary > 55000;
Example 2 Consider the query “ Find the pid and name of each person p who
(1) has both the AI and Programming and (2) knows at least 5 persons, and
report the number of persons who know p.”3
select p.pid, p.pname, (select cardinality(kp.persons)
from isKnownByPersons kp
where kp.pid = p.pid) as ct_knownByPersons
from person p
where p.pid in (select ps.pid
from personHasSkills ps
where subset(’”AI”, “Programming”’, ps.skills)) and
cardinality((select kp.persons
from knowsPersons kp
where kp.pid = p.pid)) >= 5;
Example 3 Consider the query “Find the pid and name of each person along
with the set of his of her skills that are not among the skills of persons who
work for ‘Netflix’”.4
select p.pid, p.pname, set difference((select ps.skills
from personHasSkills ps
where ps.pid = p.pid),
array(select unnest(ps.skills)
from personHasSkills ps
where is in(ps.pid, (select employees
from companyHasEmployees
where cname = ’Netflix’))))
from person p;
1. Formulate the following queries in object-relational SQL.
(a) Find the cname and headquarter of each company that employs at
least two persons who each have both the AI and the Programming
job skills.
(b) Find each skill that is not a job skill of any person who works for
Yahoo or for Netflix.
(c) Find the set of companies that employ at least 3 persons who each
know at least five persons. (So this query returns only one object,
i.e., the set of companies specified in the query.)
(d) Find the pid and name of each person p along with the set of pids of
persons who (1) know p and (2) who have the AI skill but not the
Programming skill.
3
In this example, focus on the set (array) construction ’{“AI”, “Programming”}’ and the
subset predicate. Also focus on the use of cardinality function.
4
In this example, focus on (1) the set difference operation and (2) the unnest operation
followed by a set (array) construction.
5
(e) Find each pair (s1, s2) of different skills s1 and s2 such that the
number of employees who have skill s1 and who make strictly more
than 55000 is strictly less than the number of employees who have
skill s2 and who make at most 55000.
Find each (c, p) pair where c is the cname of a company and p is the
pid of a person who works for that company and who is known by
all other persons who work for that company.
Find the pid and name of each person who has all the skills of the
combined set of job skills of the highest paid persons who work for
Yahoo.
2. Find the following set of sets
{S | S ⊆ Skill ∧ |S| ≤ 3}.
I.e., this is the set consisting of each set of job skills whose size (cardinality)
is at most 3.
Reconsider Problem 2. Let
S = {S | S ⊆ Skill ∧ |S| ≤ 3}.
Find the following set of sets
{X | X ⊆ S ∧ |X| ≤ 2}.
4. Let t be a number called a threshold. We say that a (unordered) pair of
different person pids {p1, p2} co-occur with frequency at least t if there
are at least t skills that are skills of both the person with pid p1 and the
person with pid p2.
Write a function coOccur(t integer) that returns the (unordered) pairs
{p1, p2} of person pid that co-occur with frequency at least t.
Test your coOccur function for t in the range [0, 3].
5. Let A and B be sets such that A ∪ B 6= ∅. The Jaccard index J(A, B) is
defined as the quantity
|A ∩ B|
|A ∪ B|
.
The Jaccard index is a frequently used measure to determine the similarity
between two sets. Note that if A ∩ B = ∅ then J(A, B) = 0, and if A = B
then J(A, B) = 1.
Let t be a number called a threshold. We assume that t is a float in the
range [0, 1].
6
Write a function JaccardSimilar(t float) that returns the set of unordered pairs {s1, s2} of different skills such that the set of persons who
have skill s1 and the set of persons who have skill s2 have a Jaccard index
of at least t.
Test your function JaccardSimilar for the following values for t: 0, 0.25,
0.5, 0.75, and 1.
7
2 Nested Relations and Semi-structured databases
Consider the lecture on Nested relational and semi-structured databases. In that
semi-structured database and we constructed these using a PostgreSQL query
starting from the Enroll relation.
6. Write a PostgreSQL view courseGrades that creates the nested relation
of type
This view should compute for each course, the grade information of the
students enrolled in this course. In particular, for each course and for
each grade, this relation stores in a set the sids students who obtained
7. Starting from the courseGrades view in Problem 6 solve the following
queries:
(a) Find each pair (c, S) where c is the cno of a course and S is the set of
sids of students who received an ‘A’ or a ‘B’ in course c. The type of
your answer relation should be (cno : text, Students : {(sid : text)}).
(b) Find each (s, C) pairs where s is the sid of a students and C is the set
of cnos of courses in which the student received an ‘A’. The type of
your answer relation should be (sid : text, Courses : {(cno : text)}).
Find each cno c where c is a course in which all students received the
8. Write a PostgreSQL view jcourseGrades that creates a semi-structured
database which stores jsonb objects whose structure conforms with the
structure of tuples as described for the courseGrades in Problem 6.