Slide 1DESIGNING A SET OF RELATIONS (1)DESIGNING A SET OF RELATIONS (2)1. Properties of Relational Decompositions (1)Properties of Relational Decompositions (2)Slide 6Properties of Relational Decompositions (3)Properties of Relational Decompositions (4)Properties of Relational Decompositions (5)Properties of Relational Decompositions (6)Properties of Relational Decompositions (7)Properties of Relational Decompositions (8)Properties of Relational Decompositions (8)Properties of Relational Decompositions (9)Properties of Relational Decompositions (10)2. Algorithms for Relational Database Schema Design (1)Algorithms for Relational Database Schema Design (2)Algorithms for Relational Database Schema Design (3)Algorithms for Relational Database Schema Design (4)Algorithms for Relational Database Schema Design (5)Slide 21Algorithms for Relational Database Schema Design (6)Slide 23Algorithms for Relational Database Schema Design (7)Algorithms for Relational Database Schema Design (8)3. Multivalued Dependencies and Fourth Normal Form (1)Slide 27Multivalued Dependencies and Fourth Normal Form (2)Multivalued Dependencies and Fourth Normal Form (3)Multivalued Dependencies and Fourth Normal Form (4)Multivalued Dependencies and Fourth Normal Form (5)Multivalued Dependencies and Fourth Normal Form (6)Multivalued Dependencies and Fourth Normal Form (7)4. Join Dependencies and Fifth Normal Form (1)Join Dependencies and Fifth Normal Form (2)Relation SUPPLY with Join Dependency and Conversion to Fifth Normal Form5. Inclusion Dependencies (1)Inclusion Dependencies (2)6. Other Dependencies and Normal Forms (1)Other Dependencies and Normal Forms (2)Other Dependencies and Normal Forms (3)Other Dependencies and Normal Forms (4)RecapCopyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-WesleyChapter 16Relational Database Design Algorithms and Further DependenciesCopyright © 2011 Ramez Elmasri and Shamkant NavatheDESIGNING A SET OF RELATIONS (1) The Approach of Relational Synthesis (Bottom-up Design):Assumes that all possible functional dependencies are known.First constructs a minimal set of FDsThen applies algorithms that construct a target set of 3NF or BCNF relations.Additional criteria may be needed to ensure the the set of relations in a relational database are satisfactory.Copyright © 2011 Ramez Elmasri and Shamkant NavatheDESIGNING A SET OF RELATIONS (2)Goals: Lossless join property (a must)Algorithm 16.3 tests for general losslessness.Dependency preservation propertyAlgorithm 16.5 decomposes a relation into BCNF components by sacrificing the dependency preservation.Additional normal forms4NF (based on multi-valued dependencies)5NF (based on join dependencies)Copyright © 2011 Ramez Elmasri and Shamkant Navathe1. Properties of Relational Decompositions (1)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 © 2011 Ramez Elmasri and Shamkant NavatheProperties of Relational Decompositions (2)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 © 2011 Ramez Elmasri and Shamkant NavatheProperties of Relational Decompositions (2)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 from generating spurious tuplesCopyright © 2011 Ramez Elmasri and Shamkant NavatheProperties of Relational Decompositions (3)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 υ 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 © 2011 Ramez Elmasri and Shamkant NavatheProperties of Relational Decompositions (4)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)) υ . . . υ (Rm(F)))+ = F+ (See examples in Fig 15.13a and Fig 15.12)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.Copyright © 2011 Ramez Elmasri and Shamkant NavatheProperties 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)) = rNote: 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 © 2011 Ramez Elmasri and Shamkant NavatheProperties of Relational Decompositions (6)Lossless (Non-additive) Join Property of a Decomposition (cont.): Algorithm 16.3: Testing for Lossless Join Property Input: A universal relation R, a decomposition D = {R1, R2, ..., Rm} of R, and a set F of functional dependencies. 1. Create an initial matrix S with one row i for each relation Ri in D, and one column j for each attribute Aj in R.2. Set S(i,j):=bij for all matrix entries. (* each bij is a distinct symbol associated with indices (i,j) *).3. For each row i representing relation schema Ri{for each column j representing attribute Aj {if (relation Ri includes attribute
View Full Document
Unlocking...