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Lecture 1 Relational Algebra and Relational Calculus

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Unary Relational Operations ► SELECT Operation To select the EMPLOYEE tuples whose department number is four DNO = 4 (EMPLOYEE) To select the EMPLOYEE tuples whose salary is greater than $30,000 SALARY > 30,000 (EMPLOYEE)

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Unary Relational Operations ► PROJECT Operation To list each employee’s first and last name and salary, the following is used LNAME, FNAME,SALARY (EMPLOYEE)

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Select employees in dep. 4 with salaries exceeding 25000 or in dep. 5 with salaries exceeding 30000 Show the full name and salary of every employee. Show the gender and salary of every employee. Select the gender and salary of all employees in dep. 4 with salaries exceeding 25000 or in dep. 5 with salaries exceeding 30000

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Unary Relational Operations ► To retrieve the first name, last name, and salary of all employees who work in department 5, we must apply select and project operations. We can write a single relational algebra expression as follows: ► FNAME, LNAME, SALARY ( DNO=5 (EMPLOYEE)) OR We can explicitly show the sequence of operations, giving a name to each intermediate relation: ► TEMP DNO=5 (EMPLOYEE) ► R FNAME, LNAME, SALARY (TEMP)

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Slide 6- 9

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Operations From Set Theorys ► CARTESIAN (or cross product) Operation Find the cross product between female employees (Fname, LName and SSN) and dependents ► FEMALE_EMPS SEX=’F’ (EMPLOYEE) ► EMPNAMES FNAME, LNAME,SSN (FEMALE_EMPS) ► EMP_DEPENDENTS EMPNAMES x DEPENDENT

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To get employees’ dependant s, SSNs must match The rest are spurious

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► Retrieve the manager of each department we need to combine each DEPARTMENT tuple with the EMPLOYEE tuple whose SSN value matches the MGRSSN value in the department tuple We do this by using the join operation ► DEPT_MGR DEPARTMENT MGRSSN=SSN EMPLOYEE Binary Relational Operations

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► Get the locations of every department DEPT_LOCS DEPARTMENT DEPT_LOCATIONS DNUMBER=DNUMBER

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Examples of Relational Algebra Queries Q1: Retrieve the names and addresses of all employees who work for the ‘Research’ department RESEARCH_DEPT DNAME=‘Research’ (DEPARTMENT) RESEARCH_EMPS (RESEARCH_DEPT DNUMBER= DNOEMPLOYEE EMPLOYEE) RESULT FNAME, LNAME, ADDRESS (RESEARCH_EMPS) Q2: For every project located in ‘Stafford’, list the project number and the controlling department name STAFFORD_PROJS PLOCATION=‘STAFFORD’ (PROJECT) CONTR_DEPT (STAFFORD_PROJS DNUM=DNUMBER DEPARTMENT) RESULT PNUMBER, DNAME (RESEARCH_EMPS)

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Examples of Relational Algebra Queries Q3: For every project located in ‘Stafford’, list the project number, the controlling department name and the department manager’s last name, address and birth date STAFFORD_PROJS PLOCATION=‘STAFFORD’ (PROJECT) CONTR_DEPT (STAFFORD_PROJS DNUM=DNUMBER DEPARTMENT) PROJ_DEPT_MGR (CONTR_DEPT MGRSSN=SSN EMPLOYEE) RESULT PNUMBER, DNAME,LNAME, ADDRESS, BDATE (RESEARCH_EMPS)

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Examples of Relational Algebra Queries Q4: Find the names of employees who work on ALL projects controlled by department number 5 DEPT5_PROJS(PNO) PNUMBER ( DNUM=5 (PROJECT)) EMP_PROJ(SSN, PNO) ESSN, PNO (WORKS_ON) RESULT_EMP_SSNS EMP_PROJ ÷ DEPT5_PROJS RESULT FNAME, LNAME (RESULT_EMP_SSNS ESSN = SSN EMPLOYEE) Q5:Make a list of project numbers for projects that involve an employee whose last name is ‘Smith’ either as a worker or as a manager of the department that controls the project SMITHS SSN ( LNAME=‘Smith’ (EMPLOYEE)) SMITH_WORKER_PROJ PNO (WORKS_ON ESSN = SSN SMITHS) MGRS LNAME, DNUMBER (EMPLOYEE SSN=MGRSSN DEPARTMENT) SMITH_MANAGED_DEPTS (DNUM) DNUMBER ( LNAME=‘Smith’ (MGRS)) SMITH_MANAGED_PROJS (PNO) PNUMBER (SMITH_MANAGED_DEPTS DNUMBER =DNUM PROJECT) RESULT (SMITH_WORKER_PROJS SMITH_MGR_PROJS)

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► Use of the Functional operator ℱ (script f) ℱ FUNCTION ATTRIBUTE (R) ► ℱ MAX Salary (Employee) retrieves the maximum salary value from Employee ► ℱ MIN Salary (Employee) retrieves the minimum Salary value from Employee ► ℱ SUM Salary (Employee) retrieves the sum of the Salary from Employee Sometimes we want to get aggregate functions over groups of tuples (e.g. for all employees in every department separately) ► GROUPING_ATTRIBUTES ℱ FUNCTION ATTRIBUTE (R) DNO ℱ COUNT SSN, AVERAGE Salary (Employee) groups employees by DNO (department number) and computes the count of employees and average salary per department Additional Relational Operations

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R (DNO, NO_OF_EMPLOYEES, AVERAGE_SAL ) ( DNO ℱ COUNT SSN, AVERAGE Salary (Employee)) DNO ℱ COUNT SSN, AVERAGE Salary (Employee) If no names are specified for aggregates: FUNCTION_ATTRIBUTE ℱ COUNT SSN, AVERAGE Salary (Employee) Get the number of employees in the company and the average salary of an employee Get the number of employees and the average salary in each department Default Names

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Examples of Relational Algebra Queries ► Q6: List the names of all employees with two or more dependents T1(SSN, NO_OF_DEPTS) ESSN ℱ Count DEPENDENT_NAME (DEPENDENT) T2 NO_OF_DEPS >=2 (T1) RESULT LNAME, FNAME (T2 SSN=SSN EMPLOYEE) ► Q7: Retrieve the names of employees who have no dependents ALL_EMPS SSN (EMPLOYEE) EMPS_WITH_DEPS ( SSN ) ESSN ( DEPENDENT ) EMPS_WITHOUT_DEPS (ALL_EMPS - EMPS_WITH_DEPS) RESULT LNAME, FNAME (EMPS_WITHOUT_DEPS SSN=SSN EMPLOYEE)

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EMPLOYEE SSN = MGRSNN DEPARTMENT

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SSNSUPERSSN

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