1. Spring 2003 ECE569 Lecture 02.1 ECE 569 Database System Engineering Spring 2003 Yanyong Zhang www.ece.rutgers.edu/~yyzhangwww.ece.rutgers.edu/~yyzhang Course URL www.ece.rutgers.edu/~yyzhang/spring03www.ece.rutgers.edu/~yyzhang/spring03

2. Spring 2003 ECE569 Lecture 02.2 Warm up discussion  Compare and contrast database and file system l Similarity: the ability to manage persistent data l Difference: efficiency -DBMS provides index, navigation among relations, easier data access via query language (data manipulation language), transaction management,

3. Spring 2003 ECE569 Lecture 02.3 Today’s topic  Relational data model l Different data models exist: relational, network, hierarchical, object-oriented l Powerful, simple, declarative  Relational algebra

4. Spring 2003 ECE569 Lecture 02.4 Set-theoretic notion of a relation  A domain D is a set of values l colors = {red, blue, green} l age = set of positive integers less than 20 l last_name = {a-zA-Z} +  A relation over domains D1,D2,…,Dn is a subset of D1  D2  D3…  Dn.  Example R(colors, age)  {(red,1), (blue,1),(green,1), (red,2), (blue,2),(green,2), …}

5. Spring 2003 ECE569 Lecture 02.5 Set-theoretic notion of a relation (cont)  We are only interested in finite relations.  The members of a relation are called tuples.  Each relation that is a subset of the product of k domains is k-degree.  A relation can be represented as a table, where each row is a tuple and each column corresponds to one domain. PERSON (NAME, AGE) NameAge Zhang27 Merril2 Stewart40

6. Spring 2003 ECE569 Lecture 02.6 Set-theoretic notion of a relation (cont)  Because a relation is a set of tuples, the order of tuples in the table is insignificant (but the order of domains does matter). NameAge Zhang27 Merril2 Stewart40 NameAge Zhang27 Stewart40 Merril2  AgeName 27Zhang 2Merill 40Stewart 

7. Spring 2003 ECE569 Lecture 02.7 An alternative definition – set of mappings  A relation schema R = { A 1,A 2,…,A n } (no order imposed on attributes)  A relation instance of R is a finite set of mappings {  1,  2, …,  m } where  2 : R  D where D = null  dom(A 1 )  dom(A 2 )…  dom(A n ).  Each tuple i maps each attribute in tuple i to a value.  Note that attributes must be given names that are unique in a relation schema.  Under this definition, all three instances above are equivalent.

8. Spring 2003 ECE569 Lecture 02.8 Keys  A set S of attributes is a candidate key for R if l No semantically correct instance of R can include two tuples   such that  [s] = [s], and l No proper subset of S satisfies (a)  A set of attributes satisfying (a) but not necessarily (b) is a superkey.  A relation may have multiple candidate keys. One can be designated as the primary key.

9. Spring 2003 ECE569 Lecture 02.9 Example  Schema for a relation of degree four patient(name,address,balance_due,room#)  An instance of patient with three tuples that satisfies the key constraint (name is a candidate key) patientNameAddressBalance_dueRoom # Zhang1964 highland dr$5,230518 Stewart2342 K St.$25203 Brinkley2342 K St.$10,200203  No other candidate key is possible (assuming that this is a semantically correct instance of patient).

10. Spring 2003 ECE569 Lecture 02.10 Entity-Relationship model  To describe the conceptual scheme.  An entity is a thing that exists and is distinguishable.  Entity sets consist of a group of all “similar” entities.  Each entity has certain attributes.  A relationship among entity sets is an ordered list of entity sets.

11. Spring 2003 ECE569 Lecture 02.11 Example of entity-relationship model Billed AccountMade To Room# Name Address Balance Patient Payment Amount Date Diagnosed DiseaseNameTreatment From Vital Sign Pulse Blood Time

12. Spring 2003 ECE569 Lecture 02.12 Example – Healthcare DB patient(name, address, balance_due, room#) payments(name, amount, date) vital_signs(name, pulse, blood, date, time) diagnosis(patient_name, disease_name) disease(disease_name, treatment) treats(patient, doctor)

13. Spring 2003 ECE569 Lecture 02.13 Representing entity-relationship diagrams  An entity set E can be represented by a relation whose relation scheme consists of all the attributes of the entity set.  Each tuple of the relation represents one entity in the current instance of E.  A relationship R among E 1, E 2, …, E k is represented by a relation whose relation scheme consists of the attributes in the keys for each of E 1, E 2, …, E k.

14. Spring 2003 ECE569 Lecture 02.14 Relational Algebra  A set of five basic operations that map one or more relations to a new relation.  Union: R  S   t  t  R or t  S  l The set of tuples in R or S or both l The degrees of R and S must match ABC abc adc eab DE de bc FGH deb abc abb dbb R S T abc adc eab deb abb dbb R  T

15. Spring 2003 ECE569 Lecture 02.15 Relational Algebra (cont)  Difference: R - S   t  t  R and t  S  l The set of tuples in R, but not in S l The degrees of R and S must match ABC abc adc eab DE de bc FGH deb abc abb dbb R S T adc eab R - T

16. Spring 2003 ECE569 Lecture 02.16 Relational Algebra (cont)  Cartesian Product: R X S   (a 1, a 2, …, a r+s )  (a 1, a 2, …, a r )  R and (a r+1, a r+2, …, a r+s )  S  l R x S is of degree r+s where r=degree(R) and s=degree(s) l a tuple t is in R x S if its first r components match those of a tuple in R and its last s components from a tuple in S ABC abc adc eab DE de bc FGH deb abc abb dbb R S T ABCDE abcde abcbc adcde adcbc eabde eabbc R x S R.AR.BR.CS.DS.E

17. Spring 2003 ECE569 Lecture 02.17 Relational Algebra (cont)  Projection:  i1, i2, …, im (R)   (a i1, a i2, …, a im )  (a 1, a 2, …, a n )  R  l  i1, i2, …, im (R) is of degree m l A tuple t in the result is obtained by removing and/or rearranging the attributes of a tuple of R ABC abc adc eab DE de bc FGH deb abc abb dbb R S T GF ed ba bd  2,1 (T)

18. Spring 2003 ECE569 Lecture 02.18 Relational Algebra (cont)  Selection:  F (R)   t  t  R and F(t)  l  F (R) is of the same degree as R l All tuples in R that satisfy predicate F are included in result l F is a formula involving -Constants or components of the tuple – component i is denoted $I -Comparison operators,, , ,  -Logical operators and, or, not FGH deb abc abb dbb T FGH deb abb dbb  $1=d or $2=$3 (T)

19. Spring 2003 ECE569 Lecture 02.19 Examples  Find the names of all patients with a balance of more than $10,000.  Find the names of all patients that have a pulse less than 50 or have been diagnosed with hypertension.

20. Spring 2003 ECE569 Lecture 02.20 Examples (cont)  Find all patients whose treatment includes the “application of leeches”  Print the names of all pairs of patients that occupy the same hospital room and have been diagnosed with the same disease.

21. Spring 2003 ECE569 Lecture 02.21 Examples (cont)  Print the name of the patient with the highest pulse recorded today l Find all patients that had pulse measured today l Find the set of all ‘losers’, i.e., those whose pulse is less than or equal to that of some other patient l Subtract (b) from (a) and project out patient name

22. Spring 2003 ECE569 Lecture 02.22 Examples (cont)  List all patients that suffer from at least one illness that no other patient suffers from

23. Spring 2003 ECE569 Lecture 02.23 Additional Operations  Intersection: R  S   t  t  R and t  S  l The set of tuples in both R and S l The degrees of R and S must match l R  S = R – (R – S) S R R – ( R – S) R – S

24. Spring 2003 ECE569 Lecture 02.24 Additional Operations (cont)  Theta-join: R i  j S   $i  $r+j (R  S) where r = degree(R) and   , , ,   l When  is ‘=‘ operation is called equijoin.  Find patient with highest pulse

25. Spring 2003 ECE569 Lecture 02.25 Additional Operations (cont)  Natural Join: R S l An equijoin for all attributes that R and S have in common. l The shared columns originating in S are projected out l R S   i1, i2, …, im  R.A1 = S. A1 and … and R.Ak = S.Ak (R x S) where i 1, i 2, … i m is the list of all attributes of R x S, in order, except the attributes S.A 1, …, S.A k. l Example: Names of patients being treated with leeches.

26. Spring 2003 ECE569 Lecture 02.26 Sample Queries  Consider the following set of relations frequents (drinker, bar) serves (bar, beer) likes (drinker, beer)  List the drinkers that frequent at least one bar that serves a beer they like  Construct the relation should_visit(drinker,bar) consisting of all tuples where bar b serves a beer that drinker d likes.

27. Spring 2003 ECE569 Lecture 02.27 Sample Queries (cont)  List the drinkers that frequent only bars that serve some beer they like. (Assume every drinker frequents at least one bar.)  Print the drinkers that frequent no bar that serves a beer that they like

28. Spring 2003 ECE569 Lecture 02.28 Questions on Healthcare DB  Retrieve all pairs of patients that shared a room at the same time  List all patients that finished paying their bill before one of their roomates began paying theirs.  Print the names of all pairs of patients that occupy the same hospital room and have been diagnosed with the same disease.