1. ©Silberschatz, Korth and Sudarshan2.1Database System Concepts Chapter 2: Relational Model Structure of Relational Databases Relational Algebra

2. ©Silberschatz, Korth and Sudarshan2.2Database System Concepts Basic Structure Formally, given sets D 1, D 2, …. D n a relation r is a subset of D 1 x D 2 x … x D n Thus, a relation is a set of tuples (a 1, a 2, …, a n ) where each a i  D i Example: cust-name= {Jones, Smith, Curry, Lindsay} cust-street= {Main, North, Park} cust-city= {Harrison, Rye, Pittsfield} r = {(Jones, Main, Harrison), (Smith, North, Rye), (Curry, North, Rye), (Lindsay, Park, Pittsfield)} r is a relation over cust-name x cust-street x cust-city

3. ©Silberschatz, Korth and Sudarshan2.3Database System Concepts Relations are Unordered In this (mathematical) context, since a relation is a set, the order of tuples is irrelevant and may be thought of as arbitrary. In a real DBMS, tuple order is typically very important and not arbitrary.

4. ©Silberschatz, Korth and Sudarshan2.4Database System Concepts The Table: The Relation: { (A-101,Downtown,500), (A-102,Perryridge,400), (A-201,Brighton,900), : (A-305,Round Hill,350) } Table vs. Relation

5. ©Silberschatz, Korth and Sudarshan2.5Database System Concepts Attribute Types Each attribute of a relation has a name. The set of allowed values for each attribute is called the domain of the attribute. Attribute values are required to be atomic, that is, indivisible (note how this differs from ER modeling).  Multi-valued attribute values are not atomic.  Composite attribute values are not atomic.

6. ©Silberschatz, Korth and Sudarshan2.6Database System Concepts The Evil Value “Null” The special value null is an implicit member of every domain. Tuples can have a null value for some of their attributes. A null value can be interpreted in several ways:  Value is unknown  Value does not exist  Value is known and exists, but just hasn’t been entered yet The null value causes complications in the definition of many operations. We shall consider their effect later.

7. ©Silberschatz, Korth and Sudarshan2.7Database System Concepts Relation Schema Let A 1, A 2, …, A n be attributes. Then R = (A 1, A 2, …, A n ) is a relation schema. Customer-schema = (customer-name, customer-street, customer-city) Sometimes referred to as a relational schema or relational scheme. Let R be a relation schema. Then r(R) is a relation variable. customer (Customer-schema)

8. ©Silberschatz, Korth and Sudarshan2.8Database System Concepts Database A database consists of multiple relations. account-account information depositor-depositor information, i.e., who deposits into which accounts customer- customer information Storing all information as a single relation is possible, as in: bank(account-number, balance, customer-name,..) This results in:  Repetition of information (e.g. two customers own an account)  The need for null values (e.g. represent a customer without an account). Normalization (Chapter 7) deals with how to design relational schemas.

9. ©Silberschatz, Korth and Sudarshan2.9Database System Concepts E-R Diagram for the Banking Enterprise The (modified) E-R diagram from the banking enterprise:

10. ©Silberschatz, Korth and Sudarshan2.10Database System Concepts Relational Schemes for the Banking Enterprise The following relational schemes result: branch (branch-name, branch-city, assets) customer (customer-name, customer-street, customer-city) account (account-number, branch-name, balance) loan (loan-number, branch-name, amount) depositor (customer-name, account-number) borrower (customer-name, loan-number)

11. ©Silberschatz, Korth and Sudarshan2.11Database System Concepts Schema Diagram for the Banking Enterprise

12. ©Silberschatz, Korth and Sudarshan2.12Database System Concepts Query Languages Language in which user requests information from the database. Categories of languages  procedural  non-procedural “Pure” languages:  Relational Algebra (primarily procedural)  Tuple Relational Calculus (non-procedural)  Domain Relational Calculus (non-procedural) Pure languages form underlying basis of “real” query languages.

13. ©Silberschatz, Korth and Sudarshan2.13Database System Concepts Relational Algebra Procedural language (primarily) Six basic operators:  select  project  union  set difference  cartesian product  rename

14. ©Silberschatz, Korth and Sudarshan2.14Database System Concepts Relational Algebra Each operator takes one or more relations as input and gives a new relation as a result. Each operation defines:  Requirements or constraints on its’ parameters.  Attributes in the resulting relation, including their types and names.  Which tuples will be included in the result.

15. ©Silberschatz, Korth and Sudarshan2.15Database System Concepts Select Operation – Example  Relation r ABCD   1 5 12 23 7 3 10   A=B ^ D > 5 (r) ABCD   1 23 7 10

16. ©Silberschatz, Korth and Sudarshan2.16Database System Concepts Select Operation Notation:  p (r) where p is a selection predicate and r is a relation (or more generally, a relational algebra expression). Defined as:  p (r) = {t | t  r and p(t)} where p is a formula in propositional logic consisting of terms connected by:  (and),  (or),  (not), and where each term can involve the comparison operators: =, , >, , <, 

17. ©Silberschatz, Korth and Sudarshan2.17Database System Concepts Select Operation, Cont. Example of selection:  branch-name=“Perryridge ” (account) Logically, one can think of selection as performing a table scan, but technically this may or may not be the case, i.e., an index may be used.

18. ©Silberschatz, Korth and Sudarshan2.18Database System Concepts Project Operation – Example Relation r: ABC  10 20 30 40 11121112 AC  11121112 = AC  112112  A,C (r)

19. ©Silberschatz, Korth and Sudarshan2.19Database System Concepts Project Operation Notation:  A1, A2, …, Ak (r) where A 1, A 2 are attribute names and r is a relation. The result is defined as the relation of k columns obtained by erasing the columns that are not listed. Duplicate rows are removed from result, since relations are sets. Example: To eliminate the branch-name attribute of account:  account-number, balance (account)  Note, however, that account is not actually modified.

20. ©Silberschatz, Korth and Sudarshan2.20Database System Concepts Union Operation – Example Relations r, s: r  s AB  121121 AB  2323 r s AB  12131213

21. ©Silberschatz, Korth and Sudarshan2.21Database System Concepts Union Operation Notation: r  s Defined as: r  s = {t | t  r or t  s} For r  s to be valid:  r, s must have the same arity (same number of attributes)  The attribute domains must be compatible (e.g., 2nd attribute of r deals with “the same type of values” as does the 2nd attribute of s) Example: find all customers with either an account or a loan  customer-name (depositor)   customer-name (borrower)

22. ©Silberschatz, Korth and Sudarshan2.22Database System Concepts Set Difference Operation Relations r, s: r – s AB  121121 AB  2323 r s AB  1111

23. ©Silberschatz, Korth and Sudarshan2.23Database System Concepts Set Difference Operation, Cont. Notation r – s Defined as: r – s = {t | t  r and t  s} Set differences must be taken between compatible relations.  r and s must have the same arity  attribute domains of r and s must be compatible Note that there is no requirement that the attribute names be the same.  So what about attributes names in the result?  Similarly for union.

24. ©Silberschatz, Korth and Sudarshan2.24Database System Concepts Cartesian-Product Operation Relations r, s: r x s: AB  1212 AB  1111222211112222 CD  10 20 10 20 10 E aabbaabbaabbaabb CD  20 10 E aabbaabb r s

25. ©Silberschatz, Korth and Sudarshan2.25Database System Concepts Cartesian-Product Operation, Cont. Notation r x s Defined as: r x s = {tq | t  r and q  s} The attributes of r and s are assumed to be disjoint, i.e., that R  S = . If the attributes of r and s are not disjoint, then renaming must be used.  Each attributes name has its originating relations name as a prefix.  If r and s are the same relation, then the rename operation can be used.

26. ©Silberschatz, Korth and Sudarshan2.26Database System Concepts Composition of Operations Expressions can be built using multiple operations r x s  A=C (r x s) AB  1111222211112222 CD  10 20 10 20 10 E aabbaabbaabbaabb ABCDE  122122  20 aabaab

27. ©Silberschatz, Korth and Sudarshan2.27Database System Concepts Rename Operation The rename operator allows the results of an expression to be renamed. Example:  x (E) returns the expression E under the name X If a relational-algebra expression E has arity n, then  x (A1, A2, …, An) (E) returns the result of expression E under the name X, and with the attributes renamed to A 1, A2, …., An.

28. ©Silberschatz, Korth and Sudarshan2.28Database System Concepts Formal Definition A basic expression in relational algebra consists of one of the following:  A relation in the database  A constant relation Let E 1 and E 2 be relational-algebra expressions. Then the following are all also relational-algebra expressions:  E 1  E 2  E 1 - E 2  E 1 x E 2   p (E 1 ), P is a predicate on attributes in E 1   s (E 1 ), S is a list consisting of attributes in E 1   x (E 1 ), x is the new name for the result of E 1

29. ©Silberschatz, Korth and Sudarshan2.29Database System Concepts Banking Example Recall the relational schemes from the banking enterprise: branch (branch-name, branch-city, assets) customer (customer-name, customer-street, customer-city) account (account-number, branch-name, balance) loan (loan-number, branch-name, amount) depositor (customer-name, account-number) borrower (customer-name, loan-number)

30. ©Silberschatz, Korth and Sudarshan2.30Database System Concepts Example Queries Find all loans of over $1200 (a bit ambiguous). Find the loan number for each loan with an amount greater than $1200.  amount > 1200 (loan)  loan-number (  amount > 1200 (loan))

31. ©Silberschatz, Korth and Sudarshan2.31Database System Concepts Example Queries Find the names of all customers who have a loan, an account, or both.  customer-name (borrower)   customer-name (depositor)  customer-name (borrower)   customer-name (depositor) Find the names of all customers who have a loan and an account.

32. ©Silberschatz, Korth and Sudarshan2.32Database System Concepts Example Queries Find the names of all customers who have a loan at the Perryridge branch.  customer-name (  branch-name=“Perryridge” (  borrower.loan-number = loan.loan-number (borrower x loan))) Notes:  The two selections could have been combined into one.  The selection on branch-name could have been applied to loan first, as shown on the next slide…

33. ©Silberschatz, Korth and Sudarshan2.33Database System Concepts Example Queries Alternative - Find the names of all customers who have a loan at the Perryridge branch.  customer-name (  loan.loan-number = borrower.loan-number ( borrower x  branch-name = “Perryridge” (loan))) Notes:  What are the implications of doing the selection first?  How does a non-Perryridge borrower get eliminated?  Couldn’t the amount and the branch-name attributes be eliminated from loan after the selection?  What would be the implications?

34. ©Silberschatz, Korth and Sudarshan2.34Database System Concepts Example Queries Find the names of all customers who have a loan at the Perryridge branch but no account at any branch of the bank.  customer-name (  branch-name = “Perryridge” (  borrower.loan-number = loan.loan-number (borrower x loan))) –  customer-name (depositor)

35. ©Silberschatz, Korth and Sudarshan2.35Database System Concepts Example Queries Find the largest account balance.  Requires a cartesian product between account and itself, resulting in ambiguity of attribute names.  Resolved by renaming one instance of the account relation as d.  balance (account) –  account.balance (  account.balance < d.balance (account x  d (account)))

36. ©Silberschatz, Korth and Sudarshan2.36Database System Concepts Additional Operations The following operations do not add any power to relational algebra, but simplify common queries.  Set intersection  Natural join  Theta join  Division  Assignment All of the above can be defined in terms of the six basic operators.

37. ©Silberschatz, Korth and Sudarshan2.37Database System Concepts Set-Intersection Operation Notation: r  s Defined as: r  s = { t | t  r and t  s } Assume:  r, s have the same arity  attributes of r and s are compatible Note: r  s = r - (r - s)

38. ©Silberschatz, Korth and Sudarshan2.38Database System Concepts Set-Intersection Operation, Cont. Relation r, s: r  s A B  121121  2323 r s  2

39. ©Silberschatz, Korth and Sudarshan2.39Database System Concepts Natural-Join Operation Notation: r s Let r and s be relations on schemas R and S respectively. r s is a relation that:  Has all attributes in R  S  For each pair of tuples t r and t s from r and s, respectively, if t r and t s have the same value on all attributes in R  S, add a tuple t to the result, where: t has the same value as t r on attributes in R t has the same value as t s on attributes in S

40. ©Silberschatz, Korth and Sudarshan2.40Database System Concepts Natural-Join Example Relational schemes for relations r and s, respectively: R = (A, B, C, D) S = (E, B, D) Resulting schema for r s : (A, B, C, D, E) r s is defined as:  r.A, r.B, r.C, r.D, s.E (  r.B = s.B  r.D = s.D (r x s))

41. ©Silberschatz, Korth and Sudarshan2.41Database System Concepts Natural Join Example Relations r, s: Contents of r s: AB  1241212412 CD  aababaabab B 1312313123 D aaabbaaabb E  r AB  1111211112 CD  aaaabaaaab E  s

42. ©Silberschatz, Korth and Sudarshan2.42Database System Concepts Natural Join – Another Example Find the names of all customers who have a loan at the Perryridge branch. Original Expression: Using the Natural Join Operator: Specifying the join explicitly makes it look nicer, plus it helps the query optimizer.  customer-name (  branch-name=“Perryridge” (  borrower.loan-number = loan.loan-number (borrower x loan)))  customer-name (  branch-name = “Perryridge” (borrower loan))

43. ©Silberschatz, Korth and Sudarshan2.43Database System Concepts Theta-Join Operation Notation: r θ s Let r and s be relations on schemas R and S respectively. Then, r θ s is a relation that:  Has all attributes in R  S including duplicates.  For each pair of tuples t r and t s from r and s, respectively, if θ evaluates to true for t r and t s, then add a tuple t to the result, where: t has the same value as t r on attributes in R t has the same value as t s on attributes in S r θ s is defined as:  θ (r x s)

44. ©Silberschatz, Korth and Sudarshan2.44Database System Concepts Theta-Join Example Example: R = (A, B, C, D) S = (E, B, D) Resulting schema: (r.A, r.B, r.C, r.D, s.E, s.B, s.D)

45. ©Silberschatz, Korth and Sudarshan2.45Database System Concepts Theta Join – Another Example Consider the following relational schemes: Exam = (Exam#, Average) Score = (SS#, Exam#, Grade) Find the SS#s for those students who scored less than average on some exam. Along with the SS# list the exam#, exam average, and the students’ grade.  Score.SS#, Exam.Exam#, Exam.Average, Score.Grade ( Exam Exam.Exam# = Score.Exam#  Exam.Average > Score.Grade Score)

46. ©Silberschatz, Korth and Sudarshan2.46Database System Concepts Division Operation Notation: Suited to queries that include the phrase “for all” Let r and s be relations on schemas R and S respectively where S  R, and let the attributes of R and S be: R = (A 1, …, A m, B 1, …, B n ) S = (B 1, …, B n ) The result of r  s is a relation on schema R – S = (A 1, …, A m ) where: r  s = { t | t   R-S (r)   u  s ( tu  r ) } r  s

47. ©Silberschatz, Korth and Sudarshan2.47Database System Concepts Division – Example #1 Relations r, s: r  s: AB  1212 AB  1231113461212311134612 r s

48. ©Silberschatz, Korth and Sudarshan2.48Database System Concepts Division – Example #2 AB  aaaaaaaaaaaaaaaa CD  aabababbaabababb E 1111311111113111 Relations r, s: r  s: D abab E 1111 AB  aaaa C  r s ABC

49. ©Silberschatz, Korth and Sudarshan2.49Database System Concepts Division – Example #3 AB  aaaaaaaaaaaaaaaa CD  aabababbaabababb E 1111311111113111 Relations r, s: r  s: B aaaa D abab AC   E 1111 r s

50. ©Silberschatz, Korth and Sudarshan2.50Database System Concepts Division Operation (Cont.) Let r(R) and s(S) be relations, and let S  R. Then: r  s =  R-S (r) –  R-S ( (  R-S (r) x s) –  R-S,S (r)) To see why:   R-S,S (r) simply reorders attributes of r   R-S (  R-S (r) x s) –  R-S,S (r)) gives those tuples t in  R-S (r) such that for some tuple u  s, tu  r. Property:  Let q = r  s  Then q is the largest relation satisfying q x s  r

51. ©Silberschatz, Korth and Sudarshan2.51Database System Concepts Query 2  customer-name, branch-name (depositor account)   temp(branch-name) ({(“Downtown”), (“Uptown”)}) Example Queries Find all customers who have an account from both the “Downtown” and the “Uptown” branches. where CN denotes customer-name and BN denotes branch-name. Query 1  CN (  BN=“Downtown” (depositor account))   CN (  BN=“Uptown” (depositor account))

52. ©Silberschatz, Korth and Sudarshan2.52Database System Concepts Find all customers who have an account at all branches located in the city of Brooklyn. Example Queries  customer-name, branch-name (depositor account)   branch-name (  branch-city = “Brooklyn” (branch))

53. ©Silberschatz, Korth and Sudarshan2.53Database System Concepts Assignment Operation The assignment operation (  ) provides a convenient way to express complex queries.  A query is written as a sequence of assignments.  Assignment is always made to a temporary relation variable. Example: Write r  s as temp1   R-S (r) temp2   R-S ((temp1 x s) –  R-S,S (r)) result  temp1 – temp2 Exercises => 2.1, 2.5 (5 th edition) => 3.5 (3 rd edition)

54. ©Silberschatz, Korth and Sudarshan2.54Database System Concepts Extended Relational Algebra Operations Generalized Projection Outer Join Aggregate Functions

55. ©Silberschatz, Korth and Sudarshan2.55Database System Concepts Generalized Projection Extends projection by allowing arithmetic functions to be used in the projection list.  F1, F2, …, Fn (E) E is any relational-algebra expression Each of F 1, F 2, …, F n are arithmetic expressions involving constants and attributes in the schema of E. Given relation credit-info(customer-name, limit, credit-balance), find how much more each person can spend: Also determine what percentage of their credit line that they have already used.  customer-name, limit – credit-balance, (credit-balance/limit)*100 (credit-info)

56. ©Silberschatz, Korth and Sudarshan2.56Database System Concepts Aggregate Functions An aggregation function takes a collection of values and returns a single value as a result. avg- average value min- minimum value max- maximum value sum- sum of values count- number of values Other aggregate functions are provided by most DBMS vendors.

57. ©Silberschatz, Korth and Sudarshan2.57Database System Concepts The Aggregate Operator Aggregation functions are specified in relational algebra using the aggregate operator: G1, G2, …, Gn g F1( A1), F2( A2),…, Fn( An) (E)  E is any relational-algebra expression.  G 1, G 2 …, G n is a list of attributes on which to group (can be empty).  Each F i is an aggregate function.  Each A i is an attribute name.

58. ©Silberschatz, Korth and Sudarshan2.58Database System Concepts Aggregate Operation – Example Relation r: g sum(c) (r) Could also add min, max, and other aggregates to the above expression. g sum(c), max(c), min(c) (r) AB   C 7 3 10 min-C 3 sum-C 27 sum-C 27 max-C 10

59. ©Silberschatz, Korth and Sudarshan2.59Database System Concepts Aggregate Operation – Example Grouping is somewhat like sorting, although not identical. Relation account grouped by branch-name: A list of branch names and the sum of all their account balances. branch-name g sum(balance) (account) branch-nameaccount-numberbalance Perryridge Brighton Redwood A-102 A-201 A-217 A-215 A-222 400 900 750 700 branch-namebalance Perryridge Brighton Redwood 1300 1500 700

60. ©Silberschatz, Korth and Sudarshan2.60Database System Concepts Aggregate Functions (Cont.) Consider the following relational scheme: History = (Student-Name, Department, Course-Number, Grade) Give a list of student names and, for each name, list the average course grade for each department in which the student has taken classes. SmithCSE87 SmithMTH93 JonesCHM88 JonesCSE75 BrownPSY97 : student-name, department g avg(grade) ( History ) Adding count(Course-Number) would tell how many courses the student had in each department. Similarly min and max could be added. student-name, department g avg(grade), count(Course-Number), min(Grade), max(Grade) ( History )

61. ©Silberschatz, Korth and Sudarshan2.61Database System Concepts Aggregate Functions (Cont.) Neither the resulting relation nor the aggregated attributes have names. The rename operation can be used to give both names. Aggregated attributes can be renamed in the aggregate operator: branch-name g sum(balance) as sum-balance (account)

62. ©Silberschatz, Korth and Sudarshan2.62Database System Concepts Aggregate Functions and Null Values Null values are controversial. Various proposals exist in the research literature on whether null values should be allowed and, if so, how they should affect operations.  See www.dbazine.com/ofinterest/oi-articles/pascal27 for example.www.dbazine.com/ofinterest/oi-articles/pascal27 Null values can frequently be eliminated through normalization and decomposition.

63. ©Silberschatz, Korth and Sudarshan2.63Database System Concepts Aggregate Functions and Null Values How nulls are treated by relational operators:  For duplicate elimination and grouping, null is treated like any other value, i.e., two nulls are assumed to be the same.  Aggregate functions (except for count) simply ignore null values. The above rules are arbitrary, but consistent with SQL. Note how the second rule can be misleading:  Is avg(grade) actually a class average?

64. ©Silberschatz, Korth and Sudarshan2.64Database System Concepts Null Values and Expression Evaluation Null values also affect how selection predicates are evaluated:  The result of any arithmetic expression involving null is null.  Comparisons with null returns the special truth value unknown.  Value of a predicate is treated as false if it evaluates to unknown.  balance*100 > 500 (account) For more complex predicates, the following three-valued logic is used:  OR: (unknown or true)= true (unknown or false) = unknown (unknown or unknown) = unknown  AND: (true and unknown) = unknown (false and unknown) = false (unknown and unknown) = unknown  NOT: (not unknown) = unknown  (balance*100 > 500) and (branch-name = “Perryridge”) (account)

65. ©Silberschatz, Korth and Sudarshan2.65Database System Concepts Null Values and Expression Evaluation, Cont. Why doesn’t a comparison with null simply result in false?  If false was used instead of unknown, then: not (A < 5) would not be equivalent to: A >= 5 Why would this be a problem? How does a comparison with null resulting in unknown help?

66. ©Silberschatz, Korth and Sudarshan2.66Database System Concepts Outer Join An extension of the join operation that avoids loss of information. Computes the join and then adds tuples from one relation that do not match tuples in the other relation. Typically introduces null values.

67. ©Silberschatz, Korth and Sudarshan2.67Database System Concepts Outer Join – Example Relation loan: Relation borrower: customer-nameloan-number Jones Smith Hayes L-170 L-230 L-155 3000 4000 1700 loan-numberamount L-170 L-230 L-260 branch-name Downtown Redwood Perryridge

68. ©Silberschatz, Korth and Sudarshan2.68Database System Concepts Outer Join – Example Inner Join loan Borrower loan-numberamount L-170 L-230 3000 4000 customer-name Jones Smith branch-name Downtown Redwood Left Outer Join loan Borrower Jones Smith null loan-numberamount L-170 L-230 L-260 3000 4000 1700 customer-namebranch-name Downtown Redwood Perryridge

69. ©Silberschatz, Korth and Sudarshan2.69Database System Concepts Outer Join – Example Right Outer Join loan borrower Full Outer Join loan-numberamount L-170 L-230 L-155 3000 4000 null customer-name Jones Smith Hayes branch-name Downtown Redwood null loan-numberamount L-170 L-230 L-260 L-155 3000 4000 1700 null customer-name Jones Smith null Hayes branch-name Downtown Redwood Perryridge null

70. ©Silberschatz, Korth and Sudarshan2.70Database System Concepts Example Left-Outer Join Consider the following relational schemes: Student = (SS#, Address, Date-of-Birth) Grade-Point-Average = (SS#, GPA) Consider the following query: “Create a list of all student SS#’s and their GPAs. Be sure to include all students, including first semester freshman, who do not have a GPA.” Solution: Student Grade-Point-Average

71. ©Silberschatz, Korth and Sudarshan2.71Database System Concepts Modification of the Database The database contents can be modified with operations:  Deletion  Insertion  Updating These operations can all be expressed using the assignment operator.  Some can be expressed other ways too.

72. ©Silberschatz, Korth and Sudarshan2.72Database System Concepts Deletion A deletion is expressed in relational algebra by: r  r – E where r is a relation and E is a relational algebra query. The deletion of a single tuple is expressed by letting E be a constant relation containing one tuple. Only whole tuples can be deleted, not specific attribute values.

73. ©Silberschatz, Korth and Sudarshan2.73Database System Concepts r 1    branch-city = “Needham” (account branch) r 2   account-number, branch-name, balance (r 1 ) r 3   customer-name, account-number (depositor r 2 ) account  account – r 2 depositor  depositor – r 3 Deletion Examples Delete all account records with a branch name equal to Perryridge. Delete all accounts at branches located in Needham. Delete all loan records with amount in the range of 0 to 50 loan  loan –  amount  0  and amount  50 (loan) account  account –  branch-name = “Perryridge” (account)

74. ©Silberschatz, Korth and Sudarshan2.74Database System Concepts Alternative Versions Delete all accounts at branches located in Needham. Which version is preferable? r 1   branch-name (   branch-city = “Needham” (branch)) r 2   account-number (  account-number, branch-name (account) r 1 ) account  account – (account r 2 ) depositor  depositor – (depositor r 2 ) r 1  (   branch-city <> “Needham” (depositor account branch)) account   account-number, branch-name, balance (r 1 ) depositor   customer-name, account-number (r 1 )

75. ©Silberschatz, Korth and Sudarshan2.75Database System Concepts Insertion In relational algebra, an insertion is expressed by: r  r  E where r is a relation and E is a relational algebra expression. The insertion of a single tuple is expressed by letting E be a constant relation containing one tuple.

76. ©Silberschatz, Korth and Sudarshan2.76Database System Concepts r 1  (  branch-name = “Perryridge” (borrower loan)) account  account   loan-number, branch-name,200 (r 1 ) depositor  depositor   customer-name, loan-number (r 1 ) Insertion Examples Insert information in the database specifying that Smith has $1200 in account A-973 at the Perryridge branch. Provide as a gift for all loan customers at the Perryridge branch, a $200 savings account. Let the loan number serve as the account number for the new savings account. Is r 1 overly complex? account  account  {(A-973, “Perryridge”, 1200)} depositor  depositor  {(“Smith”, A-973)}

77. ©Silberschatz, Korth and Sudarshan2.77Database System Concepts Updating Generalized projection can be used to change a value in a tuple without changing all values in the tuple. r   F1, F2, …, FI, (r) Each F i is either:  The ith attribute of r, if the ith attribute is not updated, or,  An expression, involving only constants and attributes of r, which gives a new value for an attribute, when that attribute is to be updated.

78. ©Silberschatz, Korth and Sudarshan2.78Database System Concepts Update Examples Make interest payments by increasing all balances by 5 percent. Pay 6 percent interest to all accounts with balances over $10,000 and pay 5 percent interest to all others. account   AN, BN, BAL * 1.06 (  BAL  10000 (account))   AN, BN, BAL * 1.05 (  BAL  10000 (account)) account   AN, BN, BAL * 1.05 (account) where AN, BN and BAL stand for account-number, branch-name and balance, respectively.

79. ©Silberschatz, Korth and Sudarshan2.79Database System Concepts Views Views are very important, but we will not consider them until chapter 3.

80. ©Silberschatz, Korth and Sudarshan2.80Database System Concepts The employee and ft-works Relations

81. ©Silberschatz, Korth and Sudarshan2.81Database System Concepts The Result of employee ft-works

82. ©Silberschatz, Korth and Sudarshan2.82Database System Concepts The Result of employee ft-works

83. ©Silberschatz, Korth and Sudarshan2.83Database System Concepts Result of employee ft-works

84. ©Silberschatz, Korth and Sudarshan2.84Database System Concepts Result of employee ft-works

85. ©Silberschatz, Korth and Sudarshan2.85Database System Concepts Tuples Inserted Into loan and borrower

86. ©Silberschatz, Korth and Sudarshan2.86Database System Concepts Names of All Customers Who Have a Loan at the Perryridge Branch

87. ©Silberschatz, Korth and Sudarshan2.87Database System Concepts E-R Diagram

88. ©Silberschatz, Korth and Sudarshan2.88Database System Concepts The branch Relation

89. ©Silberschatz, Korth and Sudarshan2.89Database System Concepts The loan Relation

90. ©Silberschatz, Korth and Sudarshan2.90Database System Concepts The borrower Relation

91. ©Silberschatz, Korth and Sudarshan2.91Database System Concepts Determining Keys from E-R Sets Strong entity set. The primary key of the entity set becomes the primary key of the relation. Weak entity set. The primary key of the relation consists of the union of the primary key of the strong entity set and the discriminator of the weak entity set. Relationship set. The union of the primary keys of the related entity sets becomes a super key of the relation.  For binary many-to-one relationship sets, the primary key of the “many” entity set becomes the relation’s primary key.  For one-to-one relationship sets, the relation’s primary key can be that of either entity set.  For many-to-many relationship sets, the union of the primary keys becomes the relation’s primary key