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پاورپوینت کامل Chapter 7: Relational Database Design 92 اسلاید در PowerPoint

اسلاید ۴: Combine SchemasSuppose we combine borrow and loan to get bor_loan = (customer_id, loan_number, amount )Result is possible repetition of information (L-100 in example below)

اسلاید ۵: A Combined Schema Without RepetitionConsider combining loan_branch and loanloan_amt_br = (loan_number, amount, branch_name)No repetition (as suggested by example below)

اسلاید ۶: What About Smaller SchemasSuppose we had started with bor_loan. How would we know to split up (decompose) it into borrower and loanWrite a rule “if there were a schema (loan_number, amount), then loan_number would be a candidate key”Denote as a functional dependency: loan_number amountIn bor_loan, because loan_number is not a candidate key, the amount of a loan may have to be repeated. This indicates the need to decompose bor_loan.Not all decompositions are good. Suppose we decompose employee intoemployee1 = (employee_id, employee_name)employee2 = (employee_name, telephone_number, start_date)The next slide shows how we lose information — we cannot reconstruct the original employee relation — and so, this is a lossy decomposition.

اسلاید ۷: A Lossy Decomposition

اسلاید ۸: First Normal FormDomain is atomic if its elements are considered to be indivisible unitsExamples of non-atomic domains:Set of names, composite attributesIdentification numbers like CS101 that can be broken up into partsA relational schema R is in first normal form if the domains of all attributes of R are atomicNon-atomic values complicate storage and encourage redundant (repeated) storage of dataExample: Set of accounts stored with each customer, and set of owners stored with each accountWe assume all relations are in first normal form (and revisit this in Chapter 9)

اسلاید ۹: First Normal Form (Cont’d)Atomicity is actually a property of how the elements of the domain are used.Example: Strings would normally be considered indivisible Suppose that students are given roll numbers which are strings of the form CS0012 or EE1127If the first two characters are extracted to find the department, the domain of roll numbers is not atomic.Doing so is a bad idea: leads to encoding of information in application program rather than in the database.

اسلاید ۱۰: Goal — Devise a Theory for the FollowingDecide whether a particular relation R is in “good” form.In the case that a relation R is not in “good” form, decompose it into a set of relations {R1, R2, …, Rn} such that each relation is in good form the decomposition is a lossless-join decompositionOur theory is based on:functional dependenciesmultivalued dependencies

اسلاید ۱۱: Functional DependenciesConstraints on the set of legal relations.Require that the value for a certain set of attributes determines uniquely the value for another set of attributes.A functional dependency is a generalization of the notion of a key.

اسلاید ۱۲: Functional Dependencies (Cont.)Let R be a relation schema R and RThe functional dependency holds on R if and only if for any legal relations r(R), whenever any two tuples t1 and t2 of r agree on the attributes , they also agree on the attributes . That is, t1[] = t2 [] t1[ ] = t2 [ ] Example: Consider r(A,B ) with the following instance of r.On this instance, A B does NOT hold, but B A does hold. 41 537

اسلاید ۱۳: Functional Dependencies (Cont.)K is a superkey for relation schema R if and only if K RK is a candidate key for R if and only if K R, andfor no K, RFunctional dependencies allow us to express constraints that cannot be expressed using superkeys. Consider the schema:bor_loan = (customer_id, loan_number, amount ).We expect this functional dependency to hold:loan_number amountbut would not expect the following to hold: amount customer_name

اسلاید ۱۴: Use of Functional DependenciesWe use functional dependencies to:test relations to see if they are legal under a given set of functional dependencies. If a relation r is legal under a set F of functional dependencies, we say that r satisfies F.specify constraints on the set of legal relationsWe say that F holds on R if all legal relations on R satisfy the set of functional dependencies F.Note: A specific instance of a relation schema may satisfy a functional dependency even if the functional dependency does not hold on all legal instances. For example, a specific instance of loan may, by chance, satisfy amount customer_name.

اسلاید ۱۵: Functional Dependencies (Cont.)A functional dependency is trivial if it is satisfied by all instances of a relationExample: customer_name, loan_number customer_name customer_name customer_nameIn general, is trivial if

اسلاید ۱۶: Closure of a Set of Functional DependenciesGiven a set F set of functional dependencies, there are certain other functional dependencies that are logically implied by F.For example: If A B and B C, then we can infer that A CThe set of all functional dependencies logically implied by F is the closure of F.We denote the closure of F by F+.F+ is a superset of F.

اسلاید ۱۷: Boyce-Codd Normal Form is trivial (i.e., ) is a superkey for RA relation schema R is in BCNF with respect to a set F of functional dependencies if for all functional dependencies in F+ of the form where R and R, at least one of the following holds:Example schema not in BCNF:bor_loan = ( customer_id, loan_number, amount )because loan_number amount holds on bor_loan but loan_number is not a superkey

اسلاید ۱۸: Decomposing a Schema into BCNFSuppose we have a schema R and a non-trivial dependency causes a violation of BCNF.We decompose R into:(U )( R – ( – ) )In our example, = loan_number = amountand bor_loan is replaced by (U ) = ( loan_number, amount )( R – ( – ) ) = ( customer_id, loan_number )

اسلاید ۱۹: BCNF and Dependency PreservationConstraints, including functional dependencies, are costly to check in practice unless they pertain to only one relationIf it is sufficient to test only those dependencies on each individual relation of a decomposition in order to ensure that all functional dependencies hold, then that decomposition is dependency preserving.Because it is not always possible to achieve both BCNF and dependency preservation, we consider a weaker normal form, known as third normal form.

اسلاید ۲۰: Third Normal FormA relation schema R is in third normal form (3NF) if for all: in F+ at least one of the following holds: is trivial (i.e., ) is a superkey for REach attribute A in – is contained in a candidate key for R. (NOTE: each attribute may be in a different candidate key)If a relation is in BCNF it is in 3NF (since in BCNF one of the first two conditions above must hold).Third condition is a minimal relaxation of BCNF to ensure dependency preservation (will see why later).

اسلاید ۲۱: Goals of NormalizationLet R be a relation scheme with a set F of functional dependencies.Decide whether a relation scheme R is in “good” form.In the case that a relation scheme R is not in “good” form, decompose it into a set of relation scheme {R1, R2, …, Rn} such that each relation scheme is in good form the decomposition is a lossless-join decompositionPreferably, the decomposition should be dependency preserving.

اسلاید ۲۲: How good is BCNFThere are database schemas in BCNF that do not seem to be sufficiently normalized Consider a database classes (course, teacher, book ) such that (c, t, b) classes means that t is qualified to teach c, and b is a required textbook for cThe database is supposed to list for each course the set of teachers any one of which can be the course’s instructor, and the set of books, all of which are required for the course (no matter who teaches it).

اسلاید ۲۳: There are no non-trivial functional dependencies and therefore the relation is in BCNF Insertion anomalies – i.e., if Marilyn is a new teacher that can teach database, two tuples need to be inserted(database, Marilyn, DB Concepts) (database, Marilyn, Ullman)courseteacherbookdatabasedatabasedatabasedatabasedatabasedatabaseoperating systemsoperating systemsoperating systemsoperating systemsAviAviHankHankSudarshanSudarshanAviAvi PetePeteDB ConceptsUllmanDB ConceptsUllmanDB ConceptsUllmanOS ConceptsStallingsOS ConceptsStallingsclassesHow good is BCNF (Cont.)

اسلاید ۲۴: Therefore, it is better to decompose classes into:courseteacherdatabasedatabasedatabaseoperating systemsoperating systemsAviHankSudarshanAvi Jimteachescoursebookdatabasedatabaseoperating systemsoperating systemsDB ConceptsUllmanOS ConceptsShawtextThis suggests the need for higher normal forms, such as Fourth Normal Form (4NF), which we shall see later.How good is BCNF (Cont.)

اسلاید ۲۵: Functional-Dependency TheoryWe now consider the formal theory that tells us which functional dependencies are implied logically by a given set of functional dependencies.We then develop algorithms to generate lossless decompositions into BCNF and 3NFWe then develop algorithms to test if a decomposition is dependency-preserving

اسلاید ۲۶: Closure of a Set of Functional DependenciesGiven a set F set of functional dependencies, there are certain other functional dependencies that are logically implied by F.For example: If A B and B C, then we can infer that A CThe set of all functional dependencies logically implied by F is the closure of F.We denote the closure of F by F+.We can find all of F+ by applying Armstrong’s Axioms:if , then (reflexivity)if , then (augmentation)if , and , then (transitivity)These rules are sound (generate only functional dependencies that actually hold) and complete (generate all functional dependencies that hold).

اسلاید ۲۷: ExampleR = (A, B, C, G, H, I) F = { A B A C CG H CG I B H}some members of F+A H by transitivity from A B and B HAG I by augmenting A C with G, to get AG CG and then transitivity with CG I CG HI by augmenting CG I to infer CG CGI, and augmenting of CG H to infer CGI HI, and then transitivity

اسلاید ۲۸: Procedure for Computing F+To compute the closure of a set of functional dependencies F: F + = F repeat for each functional dependency f in F+ apply reflexivity and augmentation rules on f add the resulting functional dependencies to F + for each pair of functional dependencies f1and f2 in F + if f1 and f2 can be combined using transitivity then add the resulting functional dependency to F + until F + does not change any furtherNOTE: We shall see an alternative procedure for this task later

اسلاید ۲۹: Closure of Functional Dependencies (Cont.)We can further simplify manual computation of F+ by using the following additional rules.If holds and holds, then holds (union)If holds, then holds and holds (decomposition)If holds and holds, then holds (pseudotrans