Definitions

# Join (SQL)

A SQL `JOIN` clause combines records from two tables in a relational database, resulting in a new, temporary table, sometimes called a "joined table". A `JOIN` may also be thought of as a SQL operation that relates tables by means of values common between them. SQL specifies four types of `JOIN`: `INNER`, `OUTER`, `LEFT`, and `RIGHT`. In special cases, a table (base table, view, or joined table) can `JOIN` to itself in a self-join.

A programmer writes a `JOIN` predicate to identify the records for joining. If the predicate evaluates positively, the combined record is inserted into the temporary (or "joined") table. Any predicate supported by SQL can become a `JOIN`-predicate, for example, `WHERE`-clauses.

Mathematically, a `JOIN` provides the fundamental operation in relational algebra and generalizes function composition.

## Sample tables

All subsequent explanations on join types in this article make use of the following two tables. The rows in these tables serve to illustrate the effect of different types of joins and join-predicates. In the following tables, `Department.DepartmentID` is the primary key, while `Employee.DepartmentID` is a foreign key.

Department Table
DepartmentID DepartmentName
31 Sales
33 Engineering
34 Clerical
35 Marketing

Employee Table
LastName DepartmentID
Rafferty 31
Jones 33
Steinberg 33
Robinson 34
Smith 34
Jasper NULL

Note: The "Marketing" Department currently has no listed employees. Employee "Jasper" has not been assigned to any Department yet.

## Inner join

An inner join requires each record in the two joined tables to have a matching record. An inner join essentially combines the records from two tables (A and B) based on a given join-predicate. The result of the join can be defined as the outcome of first taking the Cartesian product (or cross-join) of all records in the tables (combining every record in table A with every record in table B) - then return all records which satisfy the join predicate. Actual SQL implementations will normally use other approaches where possible, since computing the Cartesian product is not very efficient. This type of join occurs most commonly in applications, and represents the default join-type.

specifies two different syntactical ways to express joins. The first, called "explicit join notation", uses the keyword `JOIN`, whereas the second uses the "implicit join notation". The implicit join notation lists the tables for joining in the `FROM` clause of a `SELECT` statement, using commas to separate them. Thus, it specifies a cross-join, and the `WHERE` clause may apply additional filter-predicates. Those filter-predicates function comparably to join-predicates in the explicit notation.

One can further classify inner joins as equi-joins, as natural joins, or as cross-joins (see below).

Programmers should take special care when joining tables on columns that can contain NULL values, since NULL will never match any other value (or even NULL itself), unless the join condition explicitly uses the `IS NULL` or `IS NOT NULL` predicates.

As an example, the following query takes all the records from the Employee table and finds the matching record(s) in the Department table, based on the join predicate. The join predicate compares the values in the DepartmentID column in both tables. If it finds no match (i.e., the department-id of an employee does not match the current department-id from the Department table), then the joined record remains outside the joined table, i.e., outside the (intermediate) result of the join.

Example of an explicit inner join: SELECT * FROM employee

`      INNER JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`

Is equivalent to: SELECT * FROM employee, department WHERE employee.DepartmentID = department.DepartmentID

Explicit Inner join result:

Employee.LastName Employee.DepartmentID Department.DepartmentName Department.DepartmentID
Smith 34 Clerical 34
Jones 33 Engineering 33
Robinson 34 Clerical 34
Steinberg 33 Engineering 33
Rafferty 31 Sales 31

Notice that the employee "Jasper" and the department "Marketing" do not appear. Neither of these has any matching records in the respective other table: "Jasper" has no associated department and no employee has the department ID 35. Thus, no information on Jasper or on Marketing appears in the joined table. Depending on the desired results, this behavior may be a subtle bug. Outer joins may be used to avoid it.

## Types of inner joins

#### Equi-join

An equi-join, also known as an equijoin, is a specific type of comparator-based join, or theta join, that uses only equality comparisons in the join-predicate. Using other comparison operators (such as `<`) disqualifies a join as an equi-join. The query shown above has already provided an example of an equi-join: SELECT Employee.lastName, Employee.DepartmentID, Department.DepartmentName from Employee inner join Department on Employee.DepartmentID=Department.DepartmentID ORDER BY Employee.lastName;

The resulting joined table contains two columns named DepartmentID, one from table Employee and one from table Department

SQL:2003 does not have a specific syntax to express equi-joins, but some database engines provide a shorthand syntax: for example, MySQL and PostgreSQL support `USING(DepartmentID)` in addition to the `ON ...` syntax.

##### Natural join

A natural join offers a further specialization of equi-joins. The join predicate arises implicitly by comparing all columns in both tables that have the same column-name in the joined tables. The resulting joined table contains only one column for each pair of equally-named columns.

The above sample query for inner joins can be expressed as a natural join in the following way: SELECT * FROM employee NATURAL JOIN department

The result appears slightly different, however, because only one DepartmentID column occurs in the joined table.

DepartmentID Employee.LastName Department.DepartmentName
34 Smith Clerical
33 Jones Engineering
34 Robinson Clerical
33 Steinberg Engineering
31 Rafferty Sales

Using the NATURAL JOIN keyword to express joins can suffer from ambiguity at best, and could, in the case of poor coding or design, leave systems open to problems if schema changes occur in the database. For example, the removal, addition, or renaming of columns changes the semantics of a natural join. Thus, the safer approach involves explicitly coding the join-condition using a regular inner join, but such problems are likely to show in the cases of poor design.

The Oracle database implementation of SQL selects the appropriate column in the naturally-joined table from which to gather data. An error-message such as "ORA-25155: column used in NATURAL join cannot have qualifier" is an error to help prevent or reduce the problems that could occur may encourage checking and precise specification of the columns named in the query, and can also help in providing compile time checking (instead of errors in query).

### Cross join

A cross join, cartesian join or product provides the foundation upon which all types of inner joins operate. A cross join returns the cartesian product of the sets of records from the two joined tables. Thus, it equates to an inner join where the join-condition always evaluates to True or join-condition is absent in statement.

If A and B are two sets, then the cross join is written as A × B.

The SQL code for a cross join lists the tables for joining (`FROM`), but does not include any filtering join-predicate.

Example of an explicit cross join: SELECT * FROM employee CROSS JOIN department

Example of an implicit cross join: SELECT * FROM employee, department;

Employee.LastName Employee.DepartmentID Department.DepartmentName Department.DepartmentID
Rafferty 31 Sales 31
Jones 33 Sales 31
Steinberg 33 Sales 31
Smith 34 Sales 31
Robinson 34 Sales 31
Jasper NULL Sales 31
Rafferty 31 Engineering 33
Jones 33 Engineering 33
Steinberg 33 Engineering 33
Smith 34 Engineering 33
Robinson 34 Engineering 33
Jasper NULL Engineering 33
Rafferty 31 Clerical 34
Jones 33 Clerical 34
Steinberg 33 Clerical 34
Smith 34 Clerical 34
Robinson 34 Clerical 34
Jasper NULL Clerical 34
Rafferty 31 Marketing 35
Jones 33 Marketing 35
Steinberg 33 Marketing 35
Smith 34 Marketing 35
Robinson 34 Marketing 35
Jasper NULL Marketing 35

The cross join does not apply any predicate to filter records from the joined table. Programmers can further filter the results of a cross join by using a `WHERE` clause.

## Outer joins

An outer join does not require each record in the two joined tables to have a matching record. The joined table retains each record—even if no other matching record exists. Outer joins subdivide further into left outer joins, right outer joins, and full outer joins, depending on which table(s) one retains the rows from (left, right, or both).

(For a table to qualify as left or right its name has to appear after the `FROM` or `JOIN` keyword, respectively.)

No implicit join-notation for outer joins exists in SQL:2003.

### Left outer join

The result of a left outer join (or simply left join) for tables A and B always contains all records of the "left" table (A), even if the join-condition does not find any matching record in the "right" table (B). This means that if the `ON` clause matches 0 (zero) records in B, the join will still return a row in the result—but with NULL in each column from B. This means that a left outer join returns all the values from the left table, plus matched values from the right table (or NULL in case of no matching join predicate).

For example, this allows us to find an employee's department, but still to show the employee even when their department does not exist (contrary to the inner-join example above, where employees in non-existent departments are excluded from the result).

Example of a left outer join, with the additional result row italicized: SELECT * FROM employee LEFT OUTER JOIN department

`         ON employee.DepartmentID = department.DepartmentID`

Employee.LastName Employee.DepartmentID Department.DepartmentName Department.DepartmentID
Jones 33 Engineering 33
Rafferty 31 Sales 31
Robinson 34 Clerical 34
Smith 34 Clerical 34
Jasper NULL NULL NULL
Steinberg 33 Engineering 33

### Right outer join

A right outer join (or right join) closely resembles a left outer join, except with the tables reversed. Every record from the "right" table (B) will appear in the joined table at least once. If no matching row from the "left" table (A) exists, NULL will appear in columns from A for those records that have no match in A.

A right outer join returns all the values from the right table and matched values from the left table (NULL in case of no matching join predicate).

For example, this allows us to find each employee and their department, but still show departments that have no employees.

Example right outer join, with the additional result row italicized: SELECT * FROM employee RIGHT OUTER JOIN department

`         ON employee.DepartmentID = department.DepartmentID`

Employee.LastName Employee.DepartmentID Department.DepartmentName Department.DepartmentID
Smith 34 Clerical 34
Jones 33 Engineering 33
Robinson 34 Clerical 34
Steinberg 33 Engineering 33
Rafferty 31 Sales 31
NULL NULL Marketing 35

### Full outer join

A full outer join combines the results of both left and right outer joins. The joined table will contain all records from both tables, and fill in NULLs for missing matches on either side.

For example, this allows us to see each employee who is in a department and each department that has an employee, but also see each employee who is not part of a department and each department who doesn't have an employee.

Example full outer join:

SELECT * FROM employee

`      FULL OUTER JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`

Employee.LastName Employee.DepartmentID Department.DepartmentName Department.DepartmentID
Smith 34 Clerical 34
Jones 33 Engineering 33
Robinson 34 Clerical 34
Jasper NULL NULL NULL
Steinberg 33 Engineering 33
Rafferty 31 Sales 31
NULL NULL Marketing 35

Some database systems like db2 (version 2 and before) do not support this functionality directly, but they can emulate it through the use of left and right outer joins and unions. The same example can appear as follows: SELECT * FROM employee

`      LEFT JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`
UNION SELECT * FROM employee
`      RIGHT JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`
WHERE employee.DepartmentID IS NULL

or as follows: SELECT * FROM employee

`      LEFT JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`
UNION SELECT * FROM department
`      LEFT JOIN employee`
`         ON employee.DepartmentID = department.DepartmentID`
WHERE employee.DepartmentID IS NULL

or as follows: SELECT * FROM department

`      RIGHT JOIN employee`
`         ON employee.DepartmentID = department.DepartmentID`
UNION SELECT * FROM employee
`      RIGHT JOIN department`
`         ON employee.DepartmentID = department.DepartmentID`
WHERE employee.DepartmentID IS NULL

## Alternatives

The effect of outer joins can also be obtained using correlated subqueries. For example

SELECT employee.LastName, employee.DepartmentID, department.DepartmentName FROM employee LEFT OUTER JOIN department

`         ON employee.DepartmentID = department.DepartmentID`

can also be written as

SELECT employee.LastName, employee.DepartmentID,

` (SELECT department.DepartmentName`
`   FROM department`
`  WHERE employee.DepartmentID = department.DepartmentID )`
FROM employee...........

## Implementation

Much work in database-systems has aimed at efficient implementation of joins, because relational systems commonly call for joins, yet face difficulties in optimising their efficient execution. The problem arises because (inner) joins operate both commutatively and associatively. In practice, this means that the user merely supplies the list of tables for joining and the join conditions to use, and the database system has the task of determining the most efficient way to perform the operation. A query optimizer determines how to execute a query containing joins. A query optimizer has two basic freedoms:

1. Join order: Because joins function commutatively and associatively, the order in which the system joins tables does not change the final result-set of the query. However, join-order does have an enormous impact on the cost of the join operation, so choosing the best join order becomes very important.
2. Join method: Given two tables and a join condition, multiple algorithms can produce the result-set of the join. Which algorithm runs most efficiently depends on the sizes of the input tables, the number of rows from each table that match the join condition, and the operations required by the rest of the query.

Many join-algorithms treat their inputs differently. One can refer to the inputs to a join as the "outer" and "inner" join operands, or "left" and "right", respectively. In the case of nested loops, for example, the database system will scan the entire inner relation for each row of the outer relation.

One can classify query-plans involving joins as follows: left-deep : using a base table (rather than another join) as the inner operand of each join in the plan right-deep : using a base table as the outer operand of each join in the plan bushy : neither left-deep nor right-deep; both inputs to a join may themselves result from joins

These names derive from the appearance of the query plan if drawn as a tree, with the outer join relation on the left and the inner relation on the right (as convention dictates).

### Join algorithms

Three fundamental algorithms exist for performing a join operation.

#### Nested loops

Use of nested loops produces the simplest join-algorithm. For each tuple in the outer join relation, the system scans the entire inner-join relation and appends any tuples that match the join-condition to the result set. Naturally, this algorithm performs poorly with large join-relations: inner or outer or both. An index on columns in the inner relation in the join-predicate can enhance performance.

The block nested loops (BNL) approach offers a refinement to this technique: for every block in the outer relation, the system scans the entire inner relation. For each match between the current inner tuple and one of the tuples in the current block of the outer relation, the system adds a tuple to the join result-set. This variant means doing more computation for each tuple of the inner relation, but far fewer scans of the inner relation.

#### Merge join

If both join relations come in order, sorted by the join attribute(s), the system can perform the join trivially, thus:

# Consider the current "group" of tuples from the inner relation; a group consists of a set of contiguous tuples in the inner relation with the same value in the join attribute.
# For each matching tuple in the current inner group, add a tuple to the join result. Once the inner group has been exhausted, advance both the inner and outer scans to the next group.

Merge joins offer one reason why many optimizers keep track of the sort order produced by query plan operators—if one or both input relations to a merge join arrives already sorted on the join attribute, the system need not perform an additional sort. Otherwise, the DBMS will need to perform the sort, usually using an external sort to avoid consuming too much memory.

#### Hash join

A hash join algorithm can only produce equi-joins. The database system pre-forms access to the tables concerned by building hash tables on the join-attributes. The lookup in hash tables operates much faster than through index trees. However, one can compare hashed values only for equality, not for other relationships.