1. 376a. Database Design Dept. of Computer Science Vassar College
Class 4 – Relational Data Model and Relational Algebra
Prof. Billibon Yoshimi
11/25/2018

2. SELECT operation (s)
s<condition>(RELATION) - select a subset of tuples from RELATION where <condition> is satisfied.
e.g. sSSN=‘ ’(EMPLOYEE), sDEPT=5(EMPLOYEE)
Degree of result is same as R.
# of relations returned <= # of relations in R.
All relations in R are evaluated.
SELECT is commutative.
Prof. Billibon Yoshimi
11/25/2018

3. PROJECT operation (s) p<list of attributes>(RELATION)
-selects <list of attributes> columns from RELATION
e.g. pSEX, SALARY(EMPLOYEE)
PROJECT removes duplicate tuples from result set.
Degree of result is = length of <list of attributes>.
If one attribute is a key of RELATION, result will have same number of relations as RELATION.
Prof. Billibon Yoshimi
11/25/2018

4. Relational Algerbra expression
Created by nesting operations or applying operations one at a time.
pFNAME,LNAME(sDNO=5(EMPLOYEE))
Or as a sequence of operations
DEP5_EMPL <-sDNO=5(EMPLOYEE)
RESULT <- pFNAME,LNAME(DEP5_EMPL)
Prof. Billibon Yoshimi
11/25/2018

5. Rename operation ( r ) rho
rS(B1, B2, .. Bn) ( R ) - attributes of R (A1, A2, … An) are mapped to their new attribute names B1, B2, … Bn.
For example:
RESULT(FIRSTNAME, LASTNAME, SALARY) <- pFNAME,LNAME,SALARY(EMPLOYEE)
Prof. Billibon Yoshimi
11/25/2018

6. Set theory operations Union, intersection and set difference.
Sets must contain same type tuples (union compatibility constraint).
Union - R1  R2 includes all tuples in R1, R2 and the intersection of R1 and R2 without duplication.
Intersection - R1  R2 tuples in both R1 and R2.
Set difference - R1 - R2 tuples in R1 but not in R2.
Prof. Billibon Yoshimi
11/25/2018

7. Set theory cont.
By convention, attributes of resulting relation have the same name as first argument.
Notes:
- UNION and INTERSECTION are commutative and associative
R1 (op) R2 = R2 (op) R1
R1 (op) ( R2 (op) R3 ) = (R1 (op) R2) op R3
Prof. Billibon Yoshimi
11/25/2018

8. Set theory cont. Set difference is not commutative
Prof. Billibon Yoshimi
11/25/2018

9. Cartesian Product (x) Also known as cross product or cross join.
No union compatibility requirement.
Q = R1 x R2 where R1 (A1..An), R2(B1..Bm)
Performs all pairs match between the two relations.
Q(A1..An,B1…Bm)
Total number of instances in Q? |R1|*|R2|
Prof. Billibon Yoshimi
11/25/2018

10. Use for these operations?
Generate a list of all the employees of department #5 and their children.
DEPT5EMPL <- sDNO=5(EMPLOYEE)
EMPNAMES <- pFNAME,LNAME,SSN(DEP5EMPL)
EMPCHILDREN <- EMPNAMES x DEPENDENT
ACTUALDEPEND <- sSSN=ESSN(EMPCHILDREN)
RESULT <- pFNAME,LNAME,DEPENDENT_NAME(ACTUALDEPEND)
Prof. Billibon Yoshimi
11/25/2018

11. Join operations ()
Product followed by select is given a special name, join, indicated by 
Joins tuples satisfying condition.
Q = R1  condition R2 if R1(A1..An) and R2 (B2..Bm)
Q(A1..An,B1..Bm) where each tuple satisfies condition.
DEP = EMPLOYEE  SSN=ESSN DEPENDENT
A tuple should only appear once in the output set. (preserving the set constraint).
Tuples with null join attributes do not appear in Q.
Prof. Billibon Yoshimi
11/25/2018

12. Theta join () If the join constraint can be specified as
cond1 and cond2 and … condn
and each condition, condi can be represented as
A1  A2
where   { =, <, , , >, }
Then join is called a theta join.
Prof. Billibon Yoshimi
11/25/2018

13. Join operations cont.
Join operation using only = condition are called EQUIJOINS. (Always have one duplicate field)
Natural join (*) removes duplicate by requiring the attributes to the = have the same name.
PROJ_DEPT <- PROJECT*r(DNAME, DNUM,MGRSSN,MGRSTARTDATE) (DEPARTMENT)
DNUM is join attribute.
Join selectivity = expected size of join/(|R1|*|R2|)
Prof. Billibon Yoshimi
11/25/2018

14. Complete set of relational algebra operations.
{s, p, r, , -, x}
Intersection can be represented in terms of union and -.
While not all of the joins are necessary, they make database operations easier.
Prof. Billibon Yoshimi
11/25/2018

15. Non relational algebra functions.
Aggregate functions ()- describe a trait of a set of tuples.
SUM, AVERAGE, MAXIMUM, MINIMUM, COUNT
<grouping attributes>  <function list> ( R )
<grouping attributes> - attributes of R (or none)
<function list> - list of <function> <attribute> pairs
Rename called to give attributes names.
For example:
DNO F COUNT SSN, AVERAGE SALARY (EMPLOYEE)
Would result in <DNO, COUNT_SSN, AVERAGE_SALARY> tuples.
Prof. Billibon Yoshimi
11/25/2018

16. Recursive closure Find everyone reporting to ‘John Borg’
1. Find John’s SSN
2. Find all SSN, SUPERSSN relations
3. Find cross 2 and 1 and project to get all SSN of John’s supervisees.
To get next level down
4. Find cross of 3 and 2 to get all supervisees supervisees.
Prof. Billibon Yoshimi
11/25/2018

17. Left Outer Join ( )
Keeps every tuple in the first, or left relation R in R S.
Example:
EMPLOYEE SSN=MGRSSNDEPARTMENT
EMPLOYEES with no matches are padded with NULLs.
Prof. Billibon Yoshimi
11/25/2018

18. Right outer join ( )and full outer join ( )
Keep respective tuples accordingly.
Prof. Billibon Yoshimi
11/25/2018

19. Outer Union
Subset of attributes from both relations are compatible (expected that compatible attributes include a key for both relations).
Prof. Billibon Yoshimi
11/25/2018

20. Let’s try a few queries
Select the names and addresses of all employees in department #4.
For all projects not in Houston, list the project, project manager’s name and address
Make a list of the names of the children whose parent report to a manager with the last name ‘Smith’
Prof. Billibon Yoshimi
11/25/2018

21. More queries How many employees have more than 1 child.
How many employees have no children?
Prof. Billibon Yoshimi
11/25/2018

22. Now to chapter 9, mapping ER and EER to relational model
How to convert from an ER or EER model (a graph) to a relational model (using tables)?
Prof. Billibon Yoshimi
11/25/2018

23. 1. Convert strong types
Create relation R that includes all simple attributes of E.
Select key of E to be key of R. Key may include several attributes.
Prof. Billibon Yoshimi
11/25/2018

24. 2. Convert weak entities
Create relation R include foreign key of E (the owner of weak entity W)
Create new primary key for R using E foreign key and weak key
Prof. Billibon Yoshimi
11/25/2018

25. 3. Convert 1:1 relations For entities S and T that participate in R.
If S participates totally in R, use S’s primary key and T as foreign key in R.
If both participate totally, combine relationships into single relation. (merge two entity types.)
Prof. Billibon Yoshimi
11/25/2018

26. 4. Convert 1:N relations S - n - R - 1 - T Use T as foreign key in S.
Each instance in S is related to at most 1 T
Prof. Billibon Yoshimi
11/25/2018

27. 5. Convert M:N relations
Create new relation S to represent R. Use primary keys of both relations as super key in S.
Attach any attributes to relation to this relation.
Prof. Billibon Yoshimi
11/25/2018

28. 6. Convert multi-valued attributes
Create a new relation.
Primary key of R and attribute, A, is primary key of new relation.
Prof. Billibon Yoshimi
11/25/2018

29. 7. Convert n-ary relations
Create new relation S.
Primary key of S contains as foreign key keys of individual entities.
If cardinality constraint of any of relations is 1, don’t add its key to the super key.
Prof. Billibon Yoshimi
11/25/2018

30. 8. For Enhanced ER Create a relationship for parent and each child.
Add primary key of parent to each child
Primary key of each child is primary key of parent.
Prof. Billibon Yoshimi
11/25/2018