DATABASE DESIGN I - 1DL300

Transcription

1 DATABASE DESIGN I - 1DL300 Autumn 2012 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. Manivasakan Sabesan- UDBL - IT - UU

5 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

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: σ pnumber= (person) Manivasakan Sabesan- UDBL - IT - UU

7 Teachers id name phone 1 Susan Barbara Ricardo 200 Relations to work on 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 Attending student course 4 DB1 4 DS 7 DS 7 DB2 Students id sname sphone 2 Barbara Jimmy NULL 7 Anna 800 FK, student_attends

8 SELECT operation - examples? 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 > = 200 Manivasakan Sabesan- UDBL - IT - UU

9 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 Lname,Fname,Salary (Employee) Manivasakan Sabesan- UDBL - IT - UU

10 Relational algebra expressions- examples? Retrieve (select) the names of the teachers whose phone number is > = 200? Is it possible in the example above to do the projection before the selection? Why or why not? Manivasakan Sabesan- UDBL - IT - UU

11 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

12 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

13 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

14 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

15 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

16 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

17 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

18 Cartesian product The result is a new relation with (3+3) attributes and (3*5) 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

19 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

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

21 Join The result is a relation with (3+3) attributes 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

22 Join? Receive the same result by using x and σ!? Why do we need if this can be done by x and σ? Manivasakan Sabesan- UDBL - IT - UU

23 Theta join Notation: R C S C is the join condition which has the form Ar As, where is one of {=, <, >,,, }. Several terms can be connected as C1 AND C2 AND Ck A join operation with this kind of general join condition is called Theta join. A F = A B C D A B C D E F R A F S E F R S

24 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

25 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

26 Natural join 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

27 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

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

29 Teachers id name phone 1 Susan Barbara Ricardo 200 Attending student course 4 DB1 4 DS 7 DS 7 DB2 A 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 FK, student_attends? Retrieve the names of the teachers teaching DB1! Manivasakan Sabesan- UDBL - IT - UU

30 Exercises on RA expressions: Relational Algebra 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

31 Boyce-Codd Normal Form - BCNF BCNF: A relation is in BCNF if: It is in 1NF Every determinant is a candidate key. Teach department course teacher Computing Science Database 1 Sara S Computer Systems Database 1 Sara S Engineering Signals and Systems Peter E Computing Science Database 2 Sven P Normalization: Decompose the relation so that after joining the new relations spurious tuples will not be generated ( lossless join decomposition )

32 Normalization to BCNF? 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