Techniques for Manipulating Relational Data By Herbert A. Evans

Definition Terms DDL (data definition language) - of a relational system is used to define the database’s attributes, tables, relationships, and indexes. DML (data manipulation language) – is used to extract, insert, and modify the information content of the database.

What is SQL? The DML that is of most interest to us is the SQL (Structured Query Language) SQL specifies the manipulation of relations by describing the results of queries, but does not give specific strategies for executing queries.

Requiring a Formal Model We need a formal model that is sufficiently powerful to allow optimization of queries. Relational algebra is that formal model!

What does relational algebra operators do? Reduce the number of tuples in a set by selecting those that satisfy some criteria (selection operators). Reduce the size of each tuple in a set by eliminating specific attributes (projection operators). Manipulate two similar sets of tuples by combining or comparing (set operators). Increase the size of each tuple by adding attributes (join and product operations).

Find all customers whose last name is “Doe” Customer account idlast Namefirst Namestreetcitystatezipcodebalance 101BlockJane345 R Cir.ApopkaFL30458-$ HamiltonCherry3230 D St.Dade CityFL30555-$ HarrisonKatherine103 L HallBrattFL30457-$ BreauxCarroll76 M St.ApopkaFL30458-$ MorehouseAnita9501 L St.HoumaLA44099-$ DoeJane123 M St.ApopkaFL30458-$ GreavesJoseph14325 N St.GodfreyIL43580-$ DoeJaneD rm 142TallahasseeFL32306-$10.55

Using selection operator to solve the previous task Relational algebra expression would be  lastName=‘DOE’ (Customer) The new relation results from a selection that has the same attributes as the input relation, but may have fewer rows.

Result of finding all customers whose last name is “Doe” account IdfirstNamelastNamestreetcitystatezipcodebalance 111JaneDoe123 M St.ApopkaFL JaneDoeD rm 142TallahasseeFL

Find all employees whose ssn is and who were employed after march 1, 1998 TimeCard ssndatestartTimeendTimestoreIdpaid /14/19998:1512:003yes /14/19998:1512:003yes /23/199914:0022:005yes /16/19998:1512:003yes /3/199910:0014:005yes /3/199915:0019:005yes

Using selection operator to solve previous task Relational algebra expression would be  ssn=‘ ’ and date > ’01-mar-1999’ (TimeCard) The new relation results from a selection that has the same attributes as the input relation, but may have fewer rows.

Result of finding all employees whose ssn is and who were employed after march 1, 1998 ssndatestartTimeendTimestoreIdpaid /23/199914:0022:005yes /3/199910:0014:005yes /3/199915:0019:005yes

List the first and last names of all customers Customer account idlast Namefirst Namestreetcitystatezipcodebalance 101BlockJane345 R Cir.ApopkaFL30458-$ HamiltonCherry3230 D St.Dade CityFL30555-$ HarrisonKatherine103 L HallBrattFL30457-$ BreauxCarroll76 M St.ApopkaFL30458-$ MorehouseAnita9501 L St.HoumaLA44099-$ DoeJane123 M St.ApopkaFL30458-$ GreavesJoseph14325 N St.GodfreyIL43580-$ DoeJaneD rm 142TallahasseeFL32306-$10.55

Using Projection Operator to Solve Previous Task Relational algebra expression would be  lastName, firstName (Customer) The equivalent SQL expression would be select lastName, firstName from Customer

Result of listing the first and last names of all customers lastNamefirstName MorehouseAnita BlockJane BreauxCarroll HamiltonCherry HarrisonCatherine DoeJane GreavesJoseph

What are Set Operators? When two relations have the same shape, that is, when the types of the attributes are the same, we can apply the usual set operators to the relations. This includes union, intersection, and difference.

Explanation of Set Operators 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. The intersection of two relations is the set of all tuples that occur in both input relations. The difference between two relations is the set of all tuples that are in the first relation but not in the second.

Set Operator Examples

Product Operators The simplest product operator is the Cartesian Product. It produces a tuple of the new relation for each combination of one tuple from the left operand and one tuple from the right operand.

Employee x TimeCard Employee ssnlastNamefirstName UnoJane ToulouseJennifer ThreatAyisha FortuneBruce FivozinskyBruce TimeCard ssndatestartTimeendTimestoreIdpaid /14/19998:1512:003yes /14/19998:1512:003yes /23/199914:0022:005yes /16/19998:1512:003yes /3/199910:0014:005yes /3/199915:0019:005yes

Partial Result of  Employee.ssn=TimeCard.ssn (Employee X TimeCard) Employee. ssnlastName firstNa me TimeCard. ssndate startTim e endTim estoreIdpaid UnoJane /14/19998:1512:003no ToulouseJie /14/19998:1512:003no UnoJane /23/199914:0022:005no ToulouseJie /14/19998:1512:003no

Join operators It is expressed as those rows in the product whose specified fields match. It puts together related objects from two relations.

Employee natural join ssn TimeCard Employee ssnlastNamefirstName UnoJane ToulouseJennifer ThreatAyisha FortuneBruce FivozinskyBruce TimeCard ssndatestartTimeendTimestoreIdpaid /14/19998:1512:003yes /14/19998:1512:003yes /23/199914:0022:005yes /16/19998:1512:003yes /3/199910:0014:005yes /3/199915:0019:005yes

Result of natural join ssn TimeCard ssnlastName firstNam edate startTim e endTim estoreIdpaid UnoJane1/14/19998:1512:003no UnoJane1/16/19998:1512:003no ToulouseJie1/14/19998:1512:003no ThreatAyisha2/23/199914:0022:005no ThreatAyisha1/3/199910:0014:005no ThreatAyisha1/3/199915:0019:005no

Division Operator It is used to find objects that match every element of another set of objects.

Example of Division operator

References Riccardi, Greg. Principles of DATABASE SYSTEMS with Internet and Java Applications: Addision Wesley, Dr. Lee’s relational algebra lecture