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Relational Algebra continues…

Relational Algebra continues…. Rename Operation. Allows us to name, and therefore to refer to, the results of relational-algebra expressions. Allows us to refer to a relation by more than one name. Example:  x ( E ) returns the expression E under the name X

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Relational Algebra continues…

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  1. Relational Algebra continues…

  2. Rename Operation Allows us to name, and therefore to refer to, the results of relational-algebra expressions. Allows us to refer to a relation by more than one name. Example: x (E) returns the expression E under the name X If a relational-algebra expression E has arity n, then returns the result of expression E under the name X, and with the attributes renamed to A1 , A2 , …., An .

  3. Composition of Operations Can build expressions using multiple operations Example: A=C(r x s) r x s A=C(r x s) A B C D E         1 1 1 1 2 2 2 2         10 10 20 10 10 10 20 10 a a b b a a b b A B C D E       10 10 20 a a b 1 2 2

  4. Banking Example branch (branch_name, branch_city, assets) customer (customer_name, customer_street, customer_city) account (account_number, branch_name, balance) loan (loan_number, branch_name, amount) depositor (customer_name, account_number) borrower(customer_name, loan_number)

  5. Example Queries Find all loans of over $1200 amount> 1200 (loan) • Find the loan number for each loan of an amount greater than $1200 loan_number (amount> 1200 (loan)) • Find the names of all customers who have a loan, an account, or both, from the bank customer_name (borrower)  customer_name (depositor)

  6. Example Queries Find the names of all customers who have a loan at the Perryridge branch. customer_name (branch_name=“Perryridge” (borrower.loan_number = loan.loan_number(borrower x loan))) • Find the names of all customers who have a loan at the Perryridge branch but do not have an account at any branch of the bank. customer_name (branch_name = “Perryridge” (borrower.loan_number = loan.loan_number(borrower x loan))) – customer_name(depositor)

  7. Additional Operations Additional Operations Set intersection Natural join Aggregation Outer Join Division All above, other than aggregation, can be expressed using basic operations we have seen earlier

  8. Set-Intersection Operation – Example Relation r, s: r s A B A B    1 2 1   2 3 r s A B  2

  9. Natural Join Operation – Example Relations r, s: • r s B D E A B C D 1 3 1 2 3 a a a b b           1 2 4 1 2      a a b a b r s A B C D E      1 1 1 1 2      a a a a b     

  10. Natural-Join Operation Let r and s be relations on schemas R and S respectively. Then, r s is a relation on schema R S obtained as follows: Consider each pair of tuples tr from r and ts from s. If tr and ts have the same value on each of the attributes in RS, add a tuple t to the result, where t has the same value as tr on r t has the same value as ts on s Example: R = (A, B, C, D) S = (E, B, D) Result schema = (A, B, C, D, E) rs is defined as:r.A, r.B, r.C, r.D, s.E (r.B = s.B  r.D = s.D (r x s)) • Notation: r s

  11. Aggregate Functions and Operations Aggregation function takes a collection of values and returns a single value as a result. avg: average valuemin: minimum valuemax: maximum valuesum: sum of valuescount: number of values Aggregate operation in relational algebra E is any relational-algebra expression G1, G2 …, Gn is a list of attributes on which to group Each Fiis an aggregate function Each Aiis an attribute name

  12. Aggregate Operation – Example Relation account grouped by branch-name: branch_name account_number balance Perryridge Perryridge Brighton Brighton Redwood A-102 A-201 A-217 A-215 A-222 400 900 750 750 700 branch_nameg sum(balance) (account) branch_name sum(balance) Perryridge Brighton Redwood 1300 1500 700

  13. Aggregate Functions (Cont.) Result of aggregation does not have a name Can use rename operation to give it a name For convenience, we permit renaming as part of aggregate operation branch_nameg sum(balance) as sum_balance (account)

  14. Q1. Consider the following relational database, where the primary keys are underlined. Give an expression in the relational algebra to express each of the following queries: • employee( person_name, street, city) • Works(person_name, company_name, salary) • company( company_name, city) • manages(person_name, manager_name)

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