Semi-join Materialization Strategy

Semi-join Materialization is a special kind of subquery materialization used for Semi-join subqueries. It actually includes two strategies:

• Materialization/lookup
• Materialization/scan

The idea

Consider a query that finds countries in Europe which have big cities:

select * from Country 
where Country.code IN (select City.Country 
                       from City 
                       where City.Population > 7*1000*1000)
      and Country.continent='Europe'

The subquery is uncorrelated, that is, we can run it independently of the upper query. The idea of semi-join materialization is to do just that, and fill a temporary table with possible values of the City.country field of big cities, and then do a join with countries in Europe:

The join can be done in two directions:

1. From the materialized table to countries in Europe
2. From countries in Europe to the materialized table

The first way involves doing a full scan on the materialized table, so we call it "Materialization-scan".

If you run a join from Countries to the materialized table, the cheapest way to find a match in the materialized table is to make a lookup on its primary key (it has one: we used it to remove duplicates). Because of that, we call the strategy "Materialization-lookup".

Semi-join materialization in action

Materialization-Scan

If we chose to look for cities with a population greater than 7 million, the optimizer will use Materialization-Scan and EXPLAIN will show this:

MariaDB [world]> explain select * from Country where Country.code IN 
  (select City.Country from City where  City.Population > 7*1000*1000);
+----+--------------+-------------+--------+--------------------+------------+---------+--------------------+------+-----------------------+
| id | select_type  | table       | type   | possible_keys      | key        | key_len | ref                | rows | Extra                 |
+----+--------------+-------------+--------+--------------------+------------+---------+--------------------+------+-----------------------+
|  1 | PRIMARY      | <subquery2> | ALL    | distinct_key       | NULL       | NULL    | NULL               |   15 |                       |
|  1 | PRIMARY      | Country     | eq_ref | PRIMARY            | PRIMARY    | 3       | world.City.Country |    1 |                       |
|  2 | MATERIALIZED | City        | range  | Population,Country | Population | 4       | NULL               |   15 | Using index condition |
+----+--------------+-------------+--------+--------------------+------------+---------+--------------------+------+-----------------------+
3 rows in set (0.01 sec)

Here, you can see:

• There are still two SELECTs (look for columns with id=1 and id=2)
• The second select (with id=2) has select_type=MATERIALIZED. This means it will be executed and its results will be stored in a temporary table with a unique key over all columns. The unique key is there to prevent the table from containing any duplicate records.
• The first select received the table name subquery2. This is the table that we got as a result of the materialization of the select with id=2.

The optimizer chose to do a full scan over the materialized table, so this is an example of a use of the Materialization-Scan strategy.

As for execution costs, we're going to read 15 rows from table City, write 15 rows to materialized table, read them back (the optimizer assumes there won't be any duplicates), and then do 15 eq_ref accesses to table Country. In total, we'll do 45 reads and 15 writes.

By comparison, if you run the EXPLAIN with semi-join optimizations disabled, you'll get this:

MariaDB [world]> explain select * from Country where Country.code IN 
  (select City.Country from City where  City.Population > 7*1000*1000);
+----+--------------------+---------+-------+--------------------+------------+---------+------+------+------------------------------------+
| id | select_type        | table   | type  | possible_keys      | key        | key_len | ref  | rows | Extra                              |
+----+--------------------+---------+-------+--------------------+------------+---------+------+------+------------------------------------+
|  1 | PRIMARY            | Country | ALL   | NULL               | NULL       | NULL    | NULL |  239 | Using where                        |
|  2 | DEPENDENT SUBQUERY | City    | range | Population,Country | Population | 4       | NULL |   15 | Using index condition; Using where |
+----+--------------------+---------+-------+--------------------+------------+---------+------+------+------------------------------------+

...which is a plan to do (239 + 239*15) = 3824 table reads.

Materialization-Lookup

Let's modify the query slightly and look for countries which have cities with a population over one millon (instead of seven):

MariaDB [world]> explain select * from Country where Country.code IN 
  (select City.Country from City where  City.Population > 1*1000*1000) ;
+----+--------------+-------------+--------+--------------------+--------------+---------+------+------+-----------------------+
| id | select_type  | table       | type   | possible_keys      | key          | key_len | ref  | rows | Extra                 |
+----+--------------+-------------+--------+--------------------+--------------+---------+------+------+-----------------------+
|  1 | PRIMARY      | Country     | ALL    | PRIMARY            | NULL         | NULL    | NULL |  239 |                       |
|  1 | PRIMARY      | <subquery2> | eq_ref | distinct_key       | distinct_key | 3       | func |    1 |                       |
|  2 | MATERIALIZED | City        | range  | Population,Country | Population   | 4       | NULL |  238 | Using index condition |
+----+--------------+-------------+--------+--------------------+--------------+---------+------+------+-----------------------+
3 rows in set (0.00 sec)

The EXPLAIN output is similar to the one which used Materialization-scan, except that:

• the <subquery2> table is accessed with the eq_ref access method
• the access uses an index named distinct_key

This means that the optimizer is planning to do index lookups into the materialized table. In other words, we're going to use the Materialization-lookup strategy.

With optimizer_switch='semijoin=off,materialization=off'), one will get this EXPLAIN:

MariaDB [world]> explain select * from Country where Country.code IN 
  (select City.Country from City where  City.Population > 1*1000*1000) ;
+----+--------------------+---------+----------------+--------------------+---------+---------+------+------+-------------+
| id | select_type        | table   | type           | possible_keys      | key     | key_len | ref  | rows | Extra       |
+----+--------------------+---------+----------------+--------------------+---------+---------+------+------+-------------+
|  1 | PRIMARY            | Country | ALL            | NULL               | NULL    | NULL    | NULL |  239 | Using where |
|  2 | DEPENDENT SUBQUERY | City    | index_subquery | Population,Country | Country | 3       | func |   18 | Using where |
+----+--------------------+---------+----------------+--------------------+---------+---------+------+------+-------------+

One can see that both plans will do a full scan on the Country table. For the second step, MariaDB will fill the materialized table (238 rows read from table City and written to the temporary table) and then do a unique key lookup for each record in table Country, which works out to 238 unique key lookups. In total, the second step will cost (239+238) = 477 reads and 238 temp.table writes.

Execution of the latter (DEPENDENT SUBQUERY) plan reads 18 rows using an index on City.Country for each record it receives for table Country. This works out to a cost of (18*239) = 4302 reads. Had there been fewer subquery invocations, this plan would have been better than the one with Materialization. By the way, MariaDB has an option to use such a query plan, too (see FirstMatch Strategy), but it did not choose it.

Subqueries with grouping

MariaDB is able to use Semi-join materialization strategy when the subquery has grouping (other semi-join strategies are not applicable in this case).

This allows for efficient execution of queries that search for the best/last element in a certain group.

For example, let's find cities that have the biggest population on their continent:

explain 
select * from City 
where City.Population in (select max(City.Population) from City, Country 
                          where City.Country=Country.Code 
                          group by Continent)
+------+--------------+-------------+------+---------------+------------+---------+----------------------------------+------+-----------------+
| id   | select_type  | table       | type | possible_keys | key        | key_len | ref                              | rows | Extra           |
+------+--------------+-------------+------+---------------+------------+---------+----------------------------------+------+-----------------+
|    1 | PRIMARY      | <subquery2> | ALL  | distinct_key  | NULL       | NULL    | NULL                             |  239 |                 |
|    1 | PRIMARY      | City        | ref  | Population    | Population | 4       | <subquery2>.max(City.Population) |    1 |                 |
|    2 | MATERIALIZED | Country     | ALL  | PRIMARY       | NULL       | NULL    | NULL                             |  239 | Using temporary |
|    2 | MATERIALIZED | City        | ref  | Country       | Country    | 3       | world.Country.Code               |   18 |                 |
+------+--------------+-------------+------+---------------+------------+---------+----------------------------------+------+-----------------+
4 rows in set (0.00 sec)

the cities are:

+------+-------------------+---------+------------+
| ID   | Name              | Country | Population |
+------+-------------------+---------+------------+
| 1024 | Mumbai (Bombay)   | IND     |   10500000 |
| 3580 | Moscow            | RUS     |    8389200 |
| 2454 | Macao             | MAC     |     437500 |
|  608 | Cairo             | EGY     |    6789479 |
| 2515 | Ciudad de México | MEX     |    8591309 |
|  206 | São Paulo        | BRA     |    9968485 |
|  130 | Sydney            | AUS     |    3276207 |
+------+-------------------+---------+------------+

Factsheet

Semi-join materialization

• Can be used for uncorrelated IN-subqueries. The subselect may use grouping and/or aggregate functions.
• Is shown in EXPLAIN as type=MATERIALIZED for the subquery, and a line with table=<subqueryN> in the parent subquery.
• Is enabled when one has both materialization=on and semijoin=on in the optimizer_switch variable.
• The materialization=on|off flag is shared with Non-semijoin materialization.