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Joins

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Relational algebra

• Recall relational algebra was the study of actions that are performed on one or more tables and give as a result another table. – The action is called an operation. – The things acted upon (tables in this case) are

known as operands.

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Basic Operations

• The basic operations were – Selection: picking rows that satisfy some

condition (predicate) from the table.– Projection: picking columns from the table.– Union, intersection and set difference: basic

set operations that apply to union-compatible tables.

– Cartesian product: concatenate two rows, one from each table; make all such combinations.

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The Join Operation• An inner join of two tables is a Cartesian product

operation followed by a selection operation (and possibly followed by a projection operation).

• If one straightforwardly implements a join, the Cartesian product intermediary can be huge.

• On the other hand, an earlier introduction of the selection condition may require a lot of searching (for matches).

• This is a reason that relational database management systems (RDBMs) can exhibit performance problems.

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Variations of the join operation

• Theta join

• Equijoin (a particular type of Theta join)

• Natural join (a projection of an Equijoin)

• Outer join (handles unmatched records differently)

• Semijoin

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Theta join (-join)• The restriction condition selecting from the Cartesian

product does not have to be an equality, it could be any comparison operator such as – Greater than (>)– Greater than or equal to (>=)– Less than (<) – Less than or equal to (<=)– Not equal to (<>)

• Using general condition to restrict the Cartesian product is known as a Theta join.

• R FS (R and S are tables, F is a condition)

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Theta Join Example• You have a table of customers who have a

budget. • You have a table of items which have a

price. • You want to advertise your items to

customers who can afford them. • The desired relationship is an inequality, a

person’s budget should be greater than the price of the item.

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Theta Join Example: Advertising to Customers who can afford an item

The tables

Note that both have fields called ID, Access may be fooled into thinking this is the basis for a relationship.

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Theta Join Example: Advertising to Customers who can afford an item

Right click on relationship line to eliminate.

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Theta Join Example: Advertising to Customers who can afford an item

Choose fields to be displayed (projection).

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Theta Join Example: Advertising to Customers who can afford an item

No condition imposed yet, just a Cartesian product with projection.

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Theta Join Example: Advertising to Customers who can afford an item

Cartesian product projected but not restricted.

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Theta Join Example: Advertising to Customers who can afford an item

Condition added. Since it’s an inequality, this is a Theta Join.

Also added Group By so the results would be grouped by Item.

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Theta Join Example: Advertising to Customers who can afford an item

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Theta Join Example: Advertising to Customers who can afford an item

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Equijoin

• The Equijoin is a special case of the Theta join in which the restriction condition is equality.

• Example: a list of orders and the people placing them.

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Equijoin Example: a list of orders and the people that placed them

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Equijoin Example: a list of orders and the people who placed them

Condition is equality, making this an Equijoin.

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Equijoin Example: a list of orders and the people who placed them

Order.CustomerID matches Customer.CustomerID even though Access is showing lastnames instead.

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The Natural Join

• Note that the previous join had both of the matching columns (Order.CustomerID and Customer.CustomerID)

• A join that projects out one of the matching columns is known as a Natural Join.

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Natural Join Example (using Wizard)

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Natural Join Example (using Wizard)

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Natural Join Example (using Wizard)

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Natural Join Example (using Wizard)

Projecting out matching column is what makes this a Natural join.

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Natural Join Example (using Wizard)

Does counts, totals etc. instead of listing individual records.

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Natural Join Example (using Wizard)

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Natural Join Example (using Wizard)

Where’s Betty Rubble?

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Semijoin• Not all of the Customers have matches in the Order

Table. – By match we mean they have no order with that particular

CustomerID.

• If we select out those rows from the Customer table that do have a match in the Order table, we have a Semijoin.

• Semijoins can be useful in distributed systems. You can cut down on the amount of information you send across the network.– There may be more processing at the other end.

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Semijoin: Customer Orders

Two tables joined, but only one displayed in results. A semijoin.

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Semijoin: Customers who have placed orders

Jane Doe appears twice.

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Semijoin: Customers who have placed orders (SQL View)

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Semijoin: DISTINCT customers who have placed orders (SQL View)

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Semijoin: DISTINCT customers who have placed orders (DataSheet View)

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Outer Join: Bringing Back Betty

• All of the previous Equijoins have been what are called Inner Joins.

• If a record from one table does not have a match in the other table, it is eliminated.

• If this elimination feature is not desired, then you want to use an Outer Join.

• The Outer Join keeps records that do not have matches.

• R S

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Access Help: Join Type

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Inner Join: Customers and orders

Inner Join

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Inner Join: Customers and orders

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Inner Join: Customers and orders

Still Inner

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Converting to Outer Join: Right Click on Relationship Line and choose Join Properties

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Join Properties dialog box

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Outer Join: Customers and orders

Was a line, now is an arrow

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Outer Join: Customers with or without orders

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Outer Join: Customers and orders

Customers who have not placed orders.

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References

• Database Systems, Rob and Coronel

• Database Systems, Connolly and Begg