Functional Dependencies

<ul style="display: flex;"><li style="flex:1">Basics of FDs </li><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Functional Dependencies T. M. Murali October 19, 21 2009 <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example <ul style="display: flex;"><li style="flex:1">Name </li><li style="flex:1">Id </li></ul>Name Id <ul style="display: flex;"><li style="flex:1">Advises </li><li style="flex:1">Advisors </li></ul>Students Favourite IConvert to relations: <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example <ul style="display: flex;"><li style="flex:1">Name </li><li style="flex:1">Id </li></ul>Name Id <ul style="display: flex;"><li style="flex:1">Advises </li><li style="flex:1">Advisors </li></ul>Students Favourite IConvert to relations: Students(Id, Name) Advisors(Id, Name) Advises(StudentId, AdvisorId) Favourite(StudentId, AdvisorId) <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example <ul style="display: flex;"><li style="flex:1">Name </li><li style="flex:1">Id </li></ul>Name Id <ul style="display: flex;"><li style="flex:1">Advises </li><li style="flex:1">Advisors </li></ul>Students Favourite IIConvert to relations: Students(Id, Name) Advisors(Id, Name) Advises(StudentId, AdvisorId) Favourite(StudentId, AdvisorId) Suppose we perversely decide to convert Students, Advises, and Favourite into one relation. Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName Can we say Id → AdvisorId? <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName Can we say Id → AdvisorId? NO! Id is not a key for the Students relation. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName IICan we say Id → AdvisorId? NO! Id is not a key for the Students relation. What is the key for the Students? <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName IICan we say Id → AdvisorId? NO! Id is not a key for the Students relation. What is the key for the Students? {Id, AdvisorId}. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName Can we say Id → AdvisorId? NO! Id is not a key for the Students relation. IIWhat is the key for the Students? {Id, AdvisorId}. Why is this relation“bad?” <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Example of a Bad Relation Students(Id, Name, AdvisorId, AdvisorName, FavouriteAdvisorId) IIIf you know a student’s Id, can you determine the values of any other attributes? Name and FavouriteAdvisorId. Id → Name Id → FavouriteAdvisorId AdvisorId → AdvisorName Can we say Id → AdvisorId? NO! Id is not a key for the Students relation. IIWhat is the key for the Students? {Id, AdvisorId}. Why is this relation“bad?” Parts of the key determine other attributes. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Motivation for Functional Dependencies IIIIReason about constraints on attributes in a relation. Procedurally determine the keys of a relation. Detect when a relation has redundant information. Improve database designs systematically using normalisation. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Definition of Functional Dependency IIf t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t. <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Definition of Functional Dependency IIIf t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t. The FD AdvisorId → AdvisorName holds in R if in every instance of R, for every pair of tuples t and u <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Definition of Functional Dependency IIIf t is a tuple in a relation R and A is an attribute of R, then tA is the value of attribute A in tuple t. The FD AdvisorId → AdvisorName holds in R if in every instance of R, for every pair of tuples t and u if tAdvisorId = uAdvisorId, then tAdvisorName = uAdvisorName .<ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>Basics of FDs <ul style="display: flex;"><li style="flex:1">Manipulating FDs </li><li style="flex:1">Closures and Keys </li><li style="flex:1">Minimal Bases </li></ul>Definition of Functional Dependencies A functional dependency (FD) on a relation R is a statement IIf two tuples in R agree on attributes A1, A2, . . . An then they agree on attribute B. INotation: A1A2 . . . An → B <ul style="display: flex;"><li style="flex:1">T. M. Murali </li><li style="flex:1">October 19, 21 2009 </li><li style="flex:1">CS 4604: Functional Dependencies </li></ul>

Functional Dependencies

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