barcode addin for excel 2007 Decomposition Algorithm in Software

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783 Decomposition Algorithm
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The analogy between 4NF and BCNF applies to the algorithm for decomposing a schema into 4NF Figure 719 shows the 4NF decomposition algorithm It is identical to the BCNF decomposition algorithm of Figure 713, except that it uses multivalued, instead of functional, dependencies and uses the restriction of D+ to Ri If we apply the algorithm of Figure 719 to BC-schema, we nd that customer-name loan-number is a nontrivial multivalued dependency, and customer-name is not a superkey for BC-schema Following the algorithm, we replace BC-schema by two schemas: Borrower-schema = (customer-name, loan-number) Customer-schema = (customer-name, customer-street, customer-city) This pair of schemas, which is in 4NF, eliminates the problem we encountered earlier with the redundancy of BC-schema
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Silberschatz Korth Sudarshan: Database System Concepts, Fourth Edition
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II Relational Databases
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7 Relational Database Design
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The McGraw Hill Companies, 2001
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Overall Database Design Process
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As was the case when we were dealing solely with functional dependencies, we are interested in decompositions that are lossless-join decompositions and that preserve dependencies The following fact about multivalued dependencies and lossless joins shows that the algorithm of Figure 719 generates only lossless-join decompositions: Let R be a relation schema, and let D be a set of functional and multivalued dependencies on R Let R1 and R2 form a decomposition of R This decomposition is a lossless-join decomposition of R if and only if at least one of the following multivalued dependencies is in D+ : R1 R2 R1 R1 R2 R2 Recall that we stated in Section 751 that, if R1 R2 R1 or R1 R2 R2 , then R1 and R2 are a lossless-join decomposition of R The preceding fact about multivalued dependencies is a more general statement about lossless joins It says that, for every lossless-join decomposition of R into two schemas R1 and R2 , one of the two dependencies R1 R2 R1 or R1 R2 R2 must hold The issue of dependency preservation when we decompose a relation becomes more complicated in the presence of multivalued dependencies Section C12 of the appendix pursues this topic
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79 More Normal Forms
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The fourth normal form is by no means the ultimate normal form As we saw earlier, multivalued dependencies help us understand and tackle some forms of repetition of information that cannot be understood in terms of functional dependencies There are types of constraints called join dependencies that generalize multivalued dependencies, and lead to another normal form called project-join normal form (PJNF) (PJNF is called fth normal form in some books) There is a class of even more general constraints, which leads to a normal form called domain-key normal form A practical problem with the use of these generalized constraints is that they are not only hard to reason with, but there is also no set of sound and complete inference rules for reasoning about the constraints Hence PJNF and domain-key normal form are used quite rarely Appendix C provides more details about these normal forms Conspicuous by its absence from our discussion of normal forms is second normal form (2NF) We have not discussed it, because it is of historical interest only We simply de ne it, and let you experiment with it in Exercise 726
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710 Overall Database Design Process
So far we have looked at detailed issues about normal forms and normalization In this section we study how normalization ts into the overall database design process Earlier in the chapter, starting in Section 74, we assumed that a relation schema R is given, and proceeded to normalize it There are several ways in which we could have come up with the schema R:
Silberschatz Korth Sudarshan: Database System Concepts, Fourth Edition
II Relational Databases
7 Relational Database Design
The McGraw Hill Companies, 2001
7
Relational-Database Design
1 R could have been generated when converting a E-R diagram to a set of tables 2 R could have been a single relation containing all attributes that are of interest The normalization process then breaks up R into smaller relations 3 R could have been the result of some ad hoc design of relations, which we then test to verify that it satis es a desired normal form In the rest of this section we examine the implications of these approaches We also examine some practical issues in database design, including denormalization for performance and examples of bad design that are not detected by normalization
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