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Understanding Relational Algebra: Operators and Their Applications in Information Manipulation

This presentation by Li Ch’i Ooi, under Professor Sin Min Lee, delves into relational algebra, a crucial concept in database management. It covers various operators including selection, projection, set operations, and join operations. Selection reduces the number of tuples based on criteria, while projection narrows down attributes. Set operators allow for manipulation of tuples across relations. Join and product operations combine tuples from different relations, emphasizing the importance of extracting meaningful information from databases. This foundational material is essential for anyone interested in data management and analysis.

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Understanding Relational Algebra: Operators and Their Applications in Information Manipulation

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  1. CS 157B Spring 2008 Prof. Sin Min Lee Presented by Li Ch’iOoi

  2. Manipulating Information with the Relational Algebra [Ch. 6.1] • Relation is a set of tuples and that each tuple in a relation has the same number and types of attributes. Relational algebra includes : • Selection Operators • Projection Operators • Set Operators • Join and product Operations

  3. Selection Operators () • Reduce the number of tuples in a set by selecting those that satisfy some criteria. • Example : lastName = ‘Doe’ (Customer) [ Select from Customer where lastName = ‘Doe’ ] Customer

  4. Projection Operators () • Reduce the size of each tuple in a set by eliminating specific attributes. • Example : lastName, firstNAme (Customer) [ project customer onto (lastName, firstName) ] Customer

  5. Set Operators (  -) • Manipulate two similar sets of tuples by combining or comparing. • Example : Rental  PreviousRental Rental PreviousRental

  6. Set Operators (  -) ...con’t • The union of two relations is a relation that contains the set of each tuple that is in at least one of the input relations. • Partial result of the Rental  PreviousRental

  7. Set Operators (  -) ...con’t • The intersection of two relations is the set of all tuples that occur in both input relations. • The intersection of the relations Rental  PreviousRental in the previous example will return an empty set. • Another example would be the intersection between the video IDs of the two tables. •  videoId (Rental)   videoId (PrevioutsRental) = Videotapes that are currently rented as well as those that have been rented before. • The set of all videotapes that have been rented previously but are not currently rented is expressed as follows:  videoId (PreviousRental) -  videoId (Rental)

  8. Join and Product Operations () • Increase the size of each tuple by adding attributes • The Cartesian product produces a tuple of the new realtion for each combination of one tuple from the left operand and one tuple from the right operand. Example : Employee  TimeCard Employee TimeCard

  9. Join and Product Operations () ...con’t • The result of this operation has 30 tuples because there are 5 Employee and 6 TimeCard. • Partial result of Cartesian product Employee  TimeCard

  10. Join and Product Operations () ...con’t • A selection of those tuples where Employee.ssn equals TimeCard.ssn can be expressed by : Employee.ssn = TimeCard.ssn (Employee  TimeCard) • This type of product is called a join. The join operation puts together related objects from two relations. • A Natural Join however is defined so that the shared attribute appears only once in the output table. • Ref. textbook Table 6.6 [natural join] vs Table 6.7 [join]

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