Relational Database Design Theory

Transcription

1 Relational Database Design Theory Informal guidelines for good relational designs Functional dependencies Normal forms and normalization 1NF, 2NF, 3NF BCNF, 4NF, 5NF Inference rules on functional dependencies Additional properties for relational decompositions Nonadditive join property Dependency preservation property 31

2 2NF, 3NF 2NF 3NF 32

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6 BCNF Boyce-Codd Normal Form Difference from 3NF: 3NF allows A to be a key attribute Every relation in BCNF is also in 3NF Most relation schemas that are in 3NF are also in BCNF but not all: 36

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9 1NF, 2NF, 3NF, BCNF Test on any nontrivial X A Violations normalization 1NF Multi-valued attributes New relation for each multi-valued attributes 2NF 3NF a) X is a super key or b) X is not a key or c) A is a key attribute a) X is a super key or c) A is a key attribute 1) partial key -> non-key attribute (partial FD) 1) or 2) Non-key attribute -> nonkey attribute (transitive FD) BCNF a) X is a super key 1) or 2) or 3) non-key -> key attribute New relation for the partial key and its dependent attributes Above and New relation for the non-key attribute and its dependent attributes Above and New relation for the non-key attribute and its dependent attributes 39

10 Relational Database Design Theory Informal guidelines for good relational designs Functional dependencies Normal forms and normalization 1NF, 2NF, 3NF BCNF, 4NF, 5NF Functional dependencies and keys Additional properties for relational decompositions Nonadditive join property Dependency preservation property 40

11 Keys and Functional Superkey Dependencies No two distinct tuples in any state r of R can have the same value for SK Functional dependency: SK R Key Superkey of R; and it is minimal (removing any attribute A from K leaves a set of attributes that is not a superkey any more) Functional dependency: K R, and for any A in K, K- {A} R does not hold Given a set of functional dependencies, can we find the keys of R? 41

12 Inference Rules for FDs Armstrong s inference rules (complete) Reflexivity rule: ify XthenX Y Augmentation rule: ifx YthenXZ YZ Transitivity rule: ifx YandY ZthenX Z Other rules Decomposition Rule: ifx YZ then: X Y and X Z Union or Additive Rule: ifx YandX Zthen: X YZ Pseudfotransitive Rule: ifx YandYW Zthen: XW Z 42

13 Inference Rules for FDs Specify a set of FDs that can be easily determined from attribute semantics Infer additional FDs using inference rules The closure of a FD set F the set of all FDs that include F as well as all FDs that can be inferred from F 43

14 Closure of attribute set The closure of attribute set X under FD set F, denoted as X+ The set of attributes that are functionally determined by X based on F How can we computationally find X+ How can we determine a set of attributes X is a key? 44

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16 Example SSN + Dnumber + {SSN, Dnumber} + {SSN, Dnumber, Ename} + 46

17 Example SSN + = {SSN, Ename, Bdate, Address, Dnumber, Dname, Dmgr_ssn} Dnumber + = {Dnumber, Dname, Dmgr_ssn} {SSN, Dnumber} + = {SSN, Ename, Bdate, Address, Dnumber, Dname, Dmgr_ssn} {SSN, Dnumber, Ename} + = {SSN, Ename, Bdate, Address, Dnumber, Dname, Dmgr_ssn} Which of these attribute sets are superkeys? Keys? 47

18 Finding Keys based on Attribute Closure If X + = R, then X is a superkey If X + = R, and (X-{A}) +!= R, then X is a key How do we find all keys given a FD set F? How do we find one key given a FD set F? 48

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20 Example Initialization K = {SSN, Ename, Bdate, Address, Dnumber, Dname, Dmgr_ssn} Decrease one attribute at a time K = {SSN, Dnumber} 50

21 Relational Database Design Theory Informal guidelines for good relational designs Functional dependencies Normal forms and normalization 1NF, 2NF, 3NF BCNF, 4NF, 5NF Functional dependencies and keys Additional properties for relational decompositions Nonadditive join property Dependency preservation property 51

22 Dependency Preservation Property Informally, given a decomposition D of R and a FD set F on R, each FD in F either appear directly in D or could be inferred Claim 1. it is always possible to find a dependency- preserving decomposition D with respect to F such that each relation Ri in D is in 3NF 52

23 Non-additive Join Property A decomposition D = {R1, R2,..., Rm} of R has the lossless (nonadditive) join property with respect to the set of FDs F on R if, for every legal relation state r, the following holds, where * is the natural join of all the relations in D: * (ππ R1 (r),..., π Rm (r)) = r lossless for loss of information, i.e. addition of spurious information How to test whether a decomposition satisfies the lossless join property? 53

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30 Successive Lossless Join Decomposition Claim 2 (Preservation of non-additivity in successive decompositions): If a decomposition D = {R1, R2,..., Rm} of R has the lossless (non-additive) join property with respect to F and if a decomposition Di = {Q1, Q2,..., Qk} of Ri has the lossless (non-additive) join property with respect to the projection of F then the decomposition D2 = {R1, R2,..., Ri-1, Q1, Q2,..., Qk, Ri+1,..., Rm} of R has the non-additive join property with respect to F. 60

31 Normalization with BCNF and Lossless Join Property

32 In Practice Relational design from ER model or existing tables/reports Normalization for 3NF or BCNF with lossless join property Sometimes normal forms are violated deliberately to achieve better performance (less join operations) 62