Chapter 16 Relational Database Design Algorithms and Further Dependencies Properties of Relational Decompositions Relation Decomposition and Insufficiency of Normal Forms Universal Relation Schema A relation schema R A1 A2 An that includes all the attributes of the database Universal relation assumption Every attribute name is unique Copyright 2007 Ramez Elmasri and Shamkant B Navathe 2 Properties of Relational Decompositions Relation Decomposition and Insufficiency of Normal Forms cont Decomposition The process of decomposing the universal relation schema R into a set of relation schemas D R1 R2 Rm that will become the relational database schema by using the functional dependencies Attribute preservation condition Each attribute in R will appear in at least one relation schema Ri in the decomposition so that no attributes are lost Copyright 2007 Ramez Elmasri and Shamkant B Navathe 3 Properties of Relational Decompositions Another goal of decomposition is to have each individual relation Ri in the decomposition D be in BCNF or 3NF Additional properties of decomposition are needed to prevent the generation of spurious tuples Copyright 2007 Ramez Elmasri and Shamkant B Navathe 4 Example spurious tuples Copyright 2007 Ramez Elmasri and Shamkant B Navathe Example spurious tuples Copyright 2007 Ramez Elmasri and Shamkant B Navathe Properties of Relational Decompositions Goals Dependency preservation property can be sacrificed Nonadditive lossless join property a must Copyright 2007 Ramez Elmasri and Shamkant B Navathe Properties of Relational Decompositions Dependency Preservation Property of a Decomposition Definition Given a set of dependencies F on R the projection of F on Ri denoted by pRi F where Ri is a subset of R is the set of dependencies X Y in F such that the attributes in X Y are all contained in Ri Hence the projection of F on each relation schema Ri in the decomposition D is the set of functional dependencies in F the closure of F such that all their left and right hand side attributes are in Ri Copyright 2007 Ramez Elmasri and Shamkant B Navathe 9 Properties of Relational Decompositions Dependency Preservation Property of a Decomposition cont Dependency Preservation Property A decomposition D R1 R2 Rm of R is dependency preserving with respect to F if the union of the projections of F on each Ri in D is equivalent to F that is R1 F Rm F F Claim 1 It is always possible to find a dependencypreserving decomposition D with respect to F such that each relation Ri in D is in 3NF Copyright 2007 Ramez Elmasri and Shamkant B Navathe 10 Properties of Relational Decompositions 5 Lossless Non additive Join Property of a Decomposition Definition Lossless join property a decomposition D R1 R2 Rm of R has the lossless nonadditive join property with respect to the set of dependencies F on R if for every relation state r of R that satisfies F the following holds where is the natural join of all the relations in D R1 r Rm r r Note The word loss in lossless refers to loss of information not to loss of tuples In fact for loss of information a better term is addition of spurious information Copyright 2007 Ramez Elmasri and Shamkant B Navathe 11 Algorithms for Relational Database Schema Design Non Additive Join Decomposition into BCNF Schemas Copyright 2007 Ramez Elmasri and Shamkant B Navathe 12 Continues Copyright 2011 Pearson Education Inc Publishing as Pearson Addison Wesley Copyright 2011 Pearson Education Inc Publishing as Pearson Addison Wesley Boyce Codd Normal Form 15 Copyright 2007 Ramez Elmasri and Shamkant B Navathe Algorithms for Relational Database Schema Design Dependency Preserving and Non Additive Join Decomposition into 3NF Schemas Copyright 2007 Ramez Elmasri and Shamkant B Navathe 16 Algorithms for Relational Database Schema Design 7 Discussion of Normalization Algorithms Problems The database designer must first specify all the relevant functional dependencies among the database attributes These algorithms are not deterministic in general It is not always possible to find a decomposition into relation schemas that preserves dependencies and allows each relation schema in the decomposition to be in BCNF instead of 3NF Copyright 2007 Ramez Elmasri and Shamkant B Navathe 17
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