The document discusses relational database design and normalization. It covers topics like functional dependencies, normal forms like first normal form, Boyce-Codd normal form and third normal form. The goal of normalization is to organize data in a database to avoid insertion, deletion and update anomalies. Normalization techniques like decomposition are used to divide tables and isolate data to achieve higher normal forms.

1. Chapter 7: Relational Database Design

7. A Lossy Decomposition 7.7 Database System Concepts - 5 th Edition, July 28, 2005.

45. BCNF Decomposition Algorithm result := { R }; done := false; compute F + ; while (not done) do if (there is a schema R i in result that is not in BCNF) then begin let    be a nontrivial functional dependency that holds on R i such that   R i is not in F + , and    = ; result := ( result – R i )  ( R i –  )  (,  ); end else done := true; Note: each R i is in BCNF, and decomposition is lossless-join. 7.45 Database System Concepts - 5 th Edition, July 28, 2005.

53. 3NF Decomposition Algorithm Let F c be a canonical cover for F; i := 0; for each functional dependency    in F c do if none of the schemas R j , 1  j  i contains   then begin i := i + 1; R i :=   end if none of the schemas R j , 1  j  i contains a candidate key for R then begin i := i + 1; R i := any candidate key for R; end return (R 1 , R 2 , ..., R i ) 7.53 Database System Concepts - 5 th Edition, July 28, 2005.

67. 4NF Decomposition Algorithm result: = { R }; done := false; compute D + ; Let D i denote the restriction of D + to R i while ( not done ) if (there is a schema R i in result that is not in 4NF) then begin let    be a nontrivial multivalued dependency that holds on R i such that   R i is not in D i , and ; result := ( result - R i )  ( R i - )  (, ); end else done := true; Note: each R i is in 4NF, and decomposition is lossless-join 7.67 Database System Concepts - 5 th Edition, July 28, 2005.

76. End of Chapter

77. Proof of Correctness of 3NF Decomposition Algorithm

82. Figure 7.5: Sample Relation r 7.82 Database System Concepts - 5 th Edition, July 28, 2005.

83. Figure 7.6 7.83 Database System Concepts - 5 th Edition, July 28, 2005.

84. Figure 7.7 7.84 Database System Concepts - 5 th Edition, July 28, 2005.

85. Figure 7.15: An Example of Redundancy in a BCNF Relation 7.85 Database System Concepts - 5 th Edition, July 28, 2005.

86. Figure 7.16: An Illegal R 2 Relation 7.86 Database System Concepts - 5 th Edition, July 28, 2005.

87. Figure 7.18: Relation of Practice Exercise 7.2 7.87 Database System Concepts - 5 th Edition, July 28, 2005.