DATABASE DESIGN I - 1DL300

Transcription

1 DATABASE DESIGN I - 1DL300 Spring 2013 An Introductory Course on Database Systems Uppsala Database Laboratory Department of Information Technology, Uppsala University, Uppsala, Sweden

2 Introduction to Relational Algebra Elmasri/Navathe ch 6 Padron-McCarthy/Risch ch 10 Silvia Stefanova Department of Information Technology Uppsala University, Uppsala, Sweden

3 Outline 1. Why and what about the Relational Algebra 2. Unary operations Select operation Project operation 3. Set operations Union Intersection Set difference (Minus) 4. Cartesian product 5. Join operator Join Natural join Outer join 6. Exercises

4 Relational algebra Relational algebra is a procedural language Operations in relational algebra takes two or more relations as arguments and return a new relation. Relational algebraic operations: Operations from set theory: Union, Intersection, Difference, Cartesian product Operations specifically introduced for the relational data model: Select, Project, Join It have been shown that the select, project, union, difference, and Cartesian product operations form a complete set. That is any other relational algebra operation can be expressed in these

5 Outline 1. Why and what about the Relational Algebra 2. Unary operations (on one relation) Select operation Project operation 3. Set operations Union Intersection Set difference (Minus) 4. Cartesian product 5. Join operator Join Natural join Outer join 6. Exercises

6 Select operation The select operator, σ, selects a specific set of tuples from a relation according to a selection condition (or selection predicate P). Notation: σ<select condition> (R) The result relation has the same number of attributes as the initial relation Example: Retrieve persons with personal number : σpnumber= (person) Person Result relation pnumber name phone pnumber name phone Susan Barbara Barbara Ricardo

7 Teachers id name phone 1 Susan Barbara Ricardo 200 Attending student course 4 DB1 4 DS 7 DS 7 DB2 FK, student_attends Exercise FK, course_taught_by FK, course_to_attend Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 Students id sname sphone 2 Barbara Jimmy NULL 7 Anna 800? Retrieve (select) teachers whose phone number is > = 200 Retrieve (select) students with the name Jimmy Retrieve (select) teachers with name Barbara and phone number is > =

8 Project operation The project operator, Π, picks out (or projects) listed columns from a relation and creates a new relation consisting of these columns. Notation: Π <attribute list> (R) The result relation is a new relation consisting of the projected columns It doesn t return the duplicates Example: Π Fname,Salary (Employee) pnumber Fname Lname Salary Susan Lund Barbara Smith Ricardo Rodrigez 2000 Result relation Fname Salary Susan 1000 Barbara 2000 Ricardo

9 Teachers id name phone 1 Susan Barbara Ricardo 200 Attending student course 4 DB1 4 DS 7 DS 7 DB2 FK, student_attends Exercise FK, course_to_attend FK, course_taught_by Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 Students id sname sphone 2 Barbara Jimmy NULL 7 Anna 800 Retrieve the names of the teachers whose phone number is > = 200? Is it possible to define previous query where the projection is done before the selection? Why or why not?

10 Outline 1. Why and what about the Relational Algebra 2. Unary operations Select operation Project operation 3. Set operations Union Intersection Set difference (Minus) 4. Cartesian product 5. Join operator Join Natural join Outer join 6. Exercises

11 Set operations Relations are required to be union compatible to be able to take part in the union, intersection and difference operations. Two relations R1 and R2 is said to be union-compatible if: R1 D1 D2... Dn and R2 D1 D2... Dn i.e. if they have the same degree and the same domains

12 Union operation The union of two union-compatible relations R and S is the set of all tuples that either occur in R, S, or in both. Notation: R S The duplicates don t exist in the union. Example: Students id sname sphone 2 Barbara Jimmy NULL 7 Anna 800 Teachers = id name phone 1 Susan Barbara Ricardo 200 id sname sphone 2 Barbara Jimmy NULL 7 Anna Susan Ricardo

13 Intersect operation The intersection of two union-compatible sets R and S, is the set of all tuples that occur in both R and S. Notation: R S Example: Students id sname sphone Teachers = id name phone id sname sphone 2 Barbara Susan Jimmy NULL 2 Barbara Anna Ricardo

14 Difference operation The difference of two union-compatible relations R and S is the set of all tuples that occur in R but not in S. Notation: R - S Example: Students - id sname sphone 2 Barbara Jimmy NULL 7 Anna 800 Teachers = id name phone 1 Susan Barbara Ricardo 200 id sname sphone

15 Outline 1. Why and what about the Relational Algebra 2. Unary operations Select operation Project operation 3. Set operations Union Intersection Set difference (Minus) 4. Cartesian product 5. Join operator Join Natural join Outer join 6. Exercises

16 Cartesian product The Cartesian product of R and S combines all tuples from R with all tuples from S. Notation: R x S Example: Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 x Teachers id name phone 1 Susan Barbara Ricardo

17 Cartesian product The result is a new relation with (3+3) attributes and (3*3) tuples Courses x Teachers cname code tid id name phone Database Design 1 DB1 1 1 Susan 100 Database Design 1 DB1 1 2 Barbara 200 Database Design 1 DB1 1 3 Ricardo 200 Database Design 2 DB2 1 1 Susan 100 Database Design 2 DB2 1 2 Barbara 200 Database Design 2 DB2 1 3 Ricardo 200 Distributed Systems DS 3 1 Susan 100 Distributed Systems DS 3 2 Barbara 200 Distributed Systems DS 3 3 Ricardo

18 Outline 1. Why and what about the Relational Algebra 2. Unary operations Select operation Project operation 3. Set operations Union Intersection Set difference (Minus) 4. Cartesian product 5. Join operator Join Natural join Outer join 6. Exercises

19 Join The join operator creates a new relation by combining tuples from two relations that satisfy a condition Notation: R <join condition> S Example: Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 tid=id Teachers id name phone 1 Susan Barbara Ricardo

20 Join The result is a relation with (3+3) attributes and only 3 rows Courses tid=id Teachers cname code tid id name phone Database Design 1 DB1 1 1 Susan 100 Database Design 1 DB1 1 2 Barbara 200 Database Design 1 DB1 1 3 Ricardo 200 Database Design 2 DB2 1 1 Susan 100 Database Design 2 DB2 1 2 Barbara 200 Database Design 2 DB2 1 3 Ricardo 200 Distributed Systems DS 3 1 Susan 100 Distributed Systems DS 3 2 Barbara 200 Distributed Systems DS 3 3 Ricardo

21 Exercice Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 x Teachers id name phone 1 Susan Barbara Ricardo 200? Receive the result obtained when Courses tid=id Teacher by using x (Cartesian product) and σ (Selection)!? Why do we need if this can be done by x and σ? Manivasakan Sabesan- UDBL - IT - UU

22 Theta join Notation: R θc S C is the join condition which is one of {=, <, >,,, }. Several terms can be connected by using AND, OR e.g. C1 AND C2 AND Ck A join operation with this kind of general join condition is called Theta join. θ A F = A B C D A B C D E F R θ A F S E F R S

23 Equijoin Notation: R C S In C the only comparison operator is = B=C = A B a a 2 4 C D 2 4 d d A B a a 2 4 C D d d d E e e e R B=C S E e e R S

24 Natural join Natural join is equivalent with the application of join to R and S with the equality condition Ar = As (i.e. an equijoin) and then removing the redundant column As in the result. Notation: R *Ar,As S Ar,As are attribute pairs that should fulfill the join condition which has the form Ar = As. R S R B=C S A a a B 2 4 C D E B=C = A B d d d e e e a a 2 4 D d d E e e

25 Natural join Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 Teachers id name phone 1 Susan Barbara Ricardo 200 Courses * tid=id Teachers cname code tid id name phone Database Design 1 DB1 1 1 Susan 100 Database Design 2 DB2 1 1 Susan 100 Distributed Systems DS 3 3 Ricardo

26 Outer join Extensions of the join operations that avoid loss of information. Computes the join and then adds tuples from one relation that do not match tuples in the other relation to the result of the join. Fills out with NULL values: NULL signifies that the value is unknown or does not exist. All comparisons involving NULL are false by definition

27 loan branch-name Downtown Redwood Perryridge Left Outer join loan-number L-230 L-260 amount borrower customer-name loan Jones Smith Hayes branch-name Downtown Redwood Perryridge loan-number L-230 L-155 borrower (left outer join) loan-number L-230 L-260 amount customer-name Jones Smith NULL loan-number L-230 NULL

28 loan branch-name Downtown Redwood Perryridge borrower customer-name Jones Smith Hayes Right Outer join loan-number L-230 L-260 loan-number L-230 L-155 amount loan borrower (full outer join) branch-name loan-number amount customer-name loan-number Downtown Redwood NULL L-230 NULL NULL Jones Smith Hayes L-230 L

29 loan branch-name Downtown Redwood Perryridge borrower customer-name Jones Smith Hayes Full Outer join loan-number L-230 L-260 loan-number L-230 L-155 amount loan borrower (full outer join) branch-name loan-number amount customer-name loan-number Downtown Redwood NULL Perryridge L-230 NULL L NULL 1700 Jones Smith Hayes NULL L-230 L-155 NULL

30 Teachers id name phone 1 Susan Barbara Ricardo 200 Attending student course 4 DB1 4 DS 7 DS 7 DB2 FK, student_attends In-class task FK, course_taught_by FK, course_to_attend Courses cname code tid Database Design 1 DB1 1 Database Design 2 DB2 1 Distributed Systems DS 3 Students id sname sphone 2 Barbara Jimmy NULL 7 Anna 800? Retrieve the names of the teachers teaching Database Design

31 Relational Algebra Task to exercise on RA expressions: T1 Find the codes of the courses taken by the student having the name Jimmy. T2 Retrieve the names and phones of the students who are taking a database course ( Database Design 1 or Database Design 2 ). T3 List the students, names and phones of the teacher Susan. T4 Retrieve the phones of the teachers who are students as well

32 Boyce-Codd Normal Form - BCNF BCNF: A relation is in BCNF if: It is in 1NF Every determinant is a candidate key. Teach nontrivial FD: daddress -> department department course teacher daddress Computing Science Database 1 Sara S A1 Computing Science Programming 1 Anna L A3 Engineering Signals and Systems Peter E E2 Computer Systems Database 1 Sven P A2 Normalization: Decompose the relation so that after joining the new relations spurious tuples will not be generated ( lossless join decomposition ) Simplified: Make a new relation from the nontrivial FD. Keep the old relation but remove the attribute(s) on the right-hand side of the nontrivial FD

33 Boyce-Codd Normal Form - BCNF Normalized to BCNF relation Teach department Computing Science Computing Science Engineering Computer Systems daddress A1 A3 E2 A2 course teacher daddress Database 1 Sara S A1 Programming 1 Anna L A3 Signals and Systems Peter E E2 Database 1 Sven P A2? Why is not correct to decompose to the following relations: (department, daddress) and (department, course teacher)?

34 Task on normalization to BCNF T Is Street in BCNF? Why or why not? How would you normalize it? Street street city length zipcode Rydsvägen Linköping Mårdtorpsgatan Linköping Storgatan Linköping Storgatan Gnesta