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Min/Max optimization without GROUP BY

MariaDB and MySQL can optimize the MIN() and MAX() functions to be a single row lookup in the following cases:

• There is only one table used in the SELECT.
• You only have constants, MIN() and MAX() in the SELECT part.
• The argument to MIN() and MAX() is a simple column reference that is part of a key.
• There is no WHERE clause or the WHERE is used with a constant for all prefix parts of the key before the argument to MIN()/MAX().
• If the argument is used in the WHERE clause, it can be be compared to a constant with < or <= in case of MAX() and with > or >= in case of MIN().

Here are some examples to clarify this. In this case we assume there is an index on columns (a,b,c)

SELECT MIN(a),MAX(a) from t1
SELECT MIN(b) FROM t1 WHERE a=const
SELECT MIN(b),MAX(b) FROM t1 WHERE a=const
SELECT MAX(c) FROM t1 WHERE a=const AND b=const
SELECT MAX(b) FROM t1 WHERE a=const AND b<const
SELECT MIN(b) FROM t1 WHERE a=const AND b>const
SELECT MIN(b) FROM t1 WHERE a=const AND b BETWEEN const AND const
SELECT MAX(b) FROM t1 WHERE a=const AND b BETWEEN const AND const

• Instead of a=const the condition a IS NULL can be used.

The above optimization also works for subqueries:

SELECT x from t2 where y= (SELECT MIN(b) FROM t1 WHERE a=const)

Cross joins, where there is no join condition for a table, can also be optimized to a few key lookups:

select min(t1.key_part_1), max(t2.key_part_1) from t1, t2

Min/Max optimization with GROUP BY

MariaDB and MySQL support loose index scan, which can speed up certain GROUP BY queries. The basic idea is that when scanning a BTREE index (the most common index type for the MariaDB storage engines) we can jump over identical values for any prefix of a key and thus speed up the scan significantly.

Loose scan is possible in the following cases:

• The query uses only one table.
• The GROUP BY part only uses indexed columns in the same order as in the index.
• The only aggregated functions in the SELECT part are MIN() and MAX() functions and all of them using the same column which is the next index part after the used GROUP BY columns.
• Partial indexed columns cannot be used (like only indexing 10 characters of a VARCHAR(20) column).

Loose scan will apply for your query if EXPLAIN shows Using index for group-by in the Extra column. In this case the optimizer will do only one extra row fetch to calculate the value for MIN() or MAX() for every unique key prefix.

The following examples assume that the table t1 has an index on (a,b,c).

SELECT a, b, MIN(c),MAX(c) FROM t1 GROUP BY a,b

See also

• MIN()
• MAX()
• MySQL manual on loose index scans