8.2.1.7 Nested Join Optimization

The syntax for expressing joins permits nested joins. The following discussion refers to the join syntax described in Section 13.2.10.2, “JOIN Syntax”.

The syntax of table_factor is extended in comparison with the SQL Standard. The latter accepts only table_reference, not a list of them inside a pair of parentheses. This is a conservative extension if we consider each comma in a list of table_reference items as equivalent to an inner join. For example:

Is equivalent to:

In MySQL, CROSS JOIN is syntactically equivalent to INNER JOIN; they can replace each other. In standard SQL, they are not equivalent. INNER JOIN is used with an ON clause; CROSS JOIN is used otherwise.

In general, parentheses can be ignored in join expressions containing only inner join operations. Consider this join expression:

After removing parentheses and grouping operations to the left, that join expression transforms into this expression:

Yet, the two expressions are not equivalent. To see this, suppose that the tables t1, t2, and t3 have the following state:

In this case, the first expression returns a result set including the rows (1,1,101,101), (2,NULL,NULL,NULL), whereas the second expression returns the rows (1,1,101,101), (2,NULL,NULL,101):

In the following example, an outer join operation is used together with an inner join operation:

That expression cannot be transformed into the following expression:

For the given table states, the two expressions return different sets of rows:

Therefore, if we omit parentheses in a join expression with outer join operators, we might change the result set for the original expression.

More exactly, we cannot ignore parentheses in the right operand of the left outer join operation and in the left operand of a right join operation. In other words, we cannot ignore parentheses for the inner table expressions of outer join operations. Parentheses for the other operand (operand for the outer table) can be ignored.

The following expression:

Is equivalent to this expression for any tables t1,t2,t3 and any condition P over attributes t2.b and t3.b:

Whenever the order of execution of join operations in a join expression (joined_table) is not from left to right, we talk about nested joins. Consider the following queries:

Those queries are considered to contain these nested joins:

In the first query, the nested join is formed with a left join operation. In the second query, it is formed with an inner join operation.

In the first query, the parentheses can be omitted: The grammatical structure of the join expression will dictate the same order of execution for join operations. For the second query, the parentheses cannot be omitted, although the join expression here can be interpreted unambiguously without them. In our extended syntax, the parentheses in (t2, t3) of the second query are required, although theoretically the query could be parsed without them: We still would have unambiguous syntactical structure for the query because LEFT JOIN and ON play the role of the left and right delimiters for the expression (t2,t3).

The preceding examples demonstrate these points:

Queries with nested outer joins are executed in the same pipeline manner as queries with inner joins. More exactly, a variation of the nested-loop join algorithm is exploited. Recall the algorithm by which the nested-loop join executes a query (see Section 8.2.1.6, “Nested-Loop Join Algorithms”). Suppose that a join query over 3 tables T1,T2,T3 has this form:

Here, P1(T1,T2) and P2(T3,T3) are some join conditions (on expressions), whereas P(T1,T2,T3) is a condition over columns of tables T1,T2,T3.

The nested-loop join algorithm would execute this query in the following manner:

FOR each row t1 in T1 {
  FOR each row t2 in T2 such that P1(t1,t2) {
    FOR each row t3 in T3 such that P2(t2,t3) {
      IF P(t1,t2,t3) {
         t:=t1||t2||t3; OUTPUT t;
      }
    }
  }
}

The notation t1||t2||t3 indicates a row constructed by concatenating the columns of rows t1, t2, and t3. In some of the following examples, NULL where a table name appears means a row in which NULL is used for each column of that table. For example, t1||t2||NULL indicates a row constructed by concatenating the columns of rows t1 and t2, and NULL for each column of t3. Such a row is said to be NULL-complemented.

Now consider a query with nested outer joins:

For this query, modify the nested-loop pattern to obtain:

FOR each row t1 in T1 {
  BOOL f1:=FALSE;
  FOR each row t2 in T2 such that P1(t1,t2) {
    BOOL f2:=FALSE;
    FOR each row t3 in T3 such that P2(t2,t3) {
      IF P(t1,t2,t3) {
        t:=t1||t2||t3; OUTPUT t;
      }
      f2=TRUE;
      f1=TRUE;
    }
    IF (!f2) {
      IF P(t1,t2,NULL) {
        t:=t1||t2||NULL; OUTPUT t;
      }
      f1=TRUE;
    }
  }
  IF (!f1) {
    IF P(t1,NULL,NULL) {
      t:=t1||NULL||NULL; OUTPUT t;
    }
  }
}

In general, for any nested loop for the first inner table in an outer join operation, a flag is introduced that is turned off before the loop and is checked after the loop. The flag is turned on when for the current row from the outer table a match from the table representing the inner operand is found. If at the end of the loop cycle the flag is still off, no match has been found for the current row of the outer table. In this case, the row is complemented by NULL values for the columns of the inner tables. The result row is passed to the final check for the output or into the next nested loop, but only if the row satisfies the join condition of all embedded outer joins.

In the example, the outer join table expressed by the following expression is embedded:

For the query with inner joins, the optimizer could choose a different order of nested loops, such as this one:

FOR each row t3 in T3 {
  FOR each row t2 in T2 such that P2(t2,t3) {
    FOR each row t1 in T1 such that P1(t1,t2) {
      IF P(t1,t2,t3) {
         t:=t1||t2||t3; OUTPUT t;
      }
    }
  }
}

For queries with outer joins, the optimizer can choose only such an order where loops for outer tables precede loops for inner tables. Thus, for our query with outer joins, only one nesting order is possible. For the following query, the optimizer evaluates two different nestings. In both nestings, T1 must be processed in the outer loop because it is used in an outer join. T2 and T3 are used in an inner join, so that join must be processed in the inner loop. However, because the join is an inner join, T2 and T3 can be processed in either order.

One nesting evaluates T2, then T3:

FOR each row t1 in T1 {
  BOOL f1:=FALSE;
  FOR each row t2 in T2 such that P1(t1,t2) {
    FOR each row t3 in T3 such that P2(t1,t3) {
      IF P(t1,t2,t3) {
        t:=t1||t2||t3; OUTPUT t;
      }
      f1:=TRUE
    }
  }
  IF (!f1) {
    IF P(t1,NULL,NULL) {
      t:=t1||NULL||NULL; OUTPUT t;
    }
  }
}

The other nesting evaluates T3, then T2:

FOR each row t1 in T1 {
  BOOL f1:=FALSE;
  FOR each row t3 in T3 such that P2(t1,t3) {
    FOR each row t2 in T2 such that P1(t1,t2) {
      IF P(t1,t2,t3) {
        t:=t1||t2||t3; OUTPUT t;
      }
      f1:=TRUE
    }
  }
  IF (!f1) {
    IF P(t1,NULL,NULL) {
      t:=t1||NULL||NULL; OUTPUT t;
    }
  }
}

When discussing the nested-loop algorithm for inner joins, we omitted some details whose impact on the performance of query execution may be huge. We did not mention so-called “pushed-down” conditions. Suppose that our WHERE condition P(T1,T2,T3) can be represented by a conjunctive formula:

P(T1,T2,T2) = C1(T1) AND C2(T2) AND C3(T3).

In this case, MySQL actually uses the following nested-loop algorithm for the execution of the query with inner joins:

FOR each row t1 in T1 such that C1(t1) {
  FOR each row t2 in T2 such that P1(t1,t2) AND C2(t2)  {
    FOR each row t3 in T3 such that P2(t2,t3) AND C3(t3) {
      IF P(t1,t2,t3) {
         t:=t1||t2||t3; OUTPUT t;
      }
    }
  }
}

You see that each of the conjuncts C1(T1), C2(T2), C3(T3) are pushed out of the most inner loop to the most outer loop where it can be evaluated. If C1(T1) is a very restrictive condition, this condition pushdown may greatly reduce the number of rows from table T1 passed to the inner loops. As a result, the execution time for the query may improve immensely.

For a query with outer joins, the WHERE condition is to be checked only after it has been found that the current row from the outer table has a match in the inner tables. Thus, the optimization of pushing conditions out of the inner nested loops cannot be applied directly to queries with outer joins. Here we must introduce conditional pushed-down predicates guarded by the flags that are turned on when a match has been encountered.

Recall this example with outer joins:

P(T1,T2,T3)=C1(T1) AND C(T2) AND C3(T3)

For that example, the nested-loop algorithm using guarded pushed-down conditions looks like this:

FOR each row t1 in T1 such that C1(t1) {
  BOOL f1:=FALSE;
  FOR each row t2 in T2
      such that P1(t1,t2) AND (f1?C2(t2):TRUE) {
    BOOL f2:=FALSE;
    FOR each row t3 in T3
        such that P2(t2,t3) AND (f1&&f2?C3(t3):TRUE) {
      IF (f1&&f2?TRUE:(C2(t2) AND C3(t3))) {
        t:=t1||t2||t3; OUTPUT t;
      }
      f2=TRUE;
      f1=TRUE;
    }
    IF (!f2) {
      IF (f1?TRUE:C2(t2) && P(t1,t2,NULL)) {
        t:=t1||t2||NULL; OUTPUT t;
      }
      f1=TRUE;
    }
  }
  IF (!f1 && P(t1,NULL,NULL)) {
      t:=t1||NULL||NULL; OUTPUT t;
  }
}

In general, pushed-down predicates can be extracted from join conditions such as P1(T1,T2) and P(T2,T3). In this case, a pushed-down predicate is guarded also by a flag that prevents checking the predicate for the NULL-complemented row generated by the corresponding outer join operation.

Access by key from one inner table to another in the same nested join is prohibited if it is induced by a predicate from the WHERE condition.