Histogram-Based Statistics

Histogram-based statistics are a mechanism to improve the query plan chosen by the optimizer in certain situations. Before their introduction, all conditions on non-indexed columns were ignored when searching for the best execution plan. Histograms can be collected for both indexed and non-indexed columns, and are made available to the optimizer.

Histogram statistics are stored in the mysql.column_stats table, which stores data for engine-independent table statistics, and so are essentially a subset of engine-independent table statistics.

Histograms are used by default from MariaDB 10.4.3 if they are available. However, histogram statistics are not automatically collected, as collection is expensive, requiring a full table scan. See Collecting Statistics with the ANALYZE TABLE Statement for details.

Consider this example, using the following query:

SELECT * FROM t1,t2 WHERE t1.a=t2.a AND t2.b BETWEEN 1 AND 3;

Let's assume that

• table t1 contains 100 records

• table t2 contains 1000 records

• there is a primary index on t1(a)

• there is a secondary index on t2(a)

• there is no index defined on column t2.b

• the selectivity of the condition t2.b BETWEEN (1,3) is high (~ 1%)

Before histograms were introduced, the optimizer would choose the plan that:

• accesses t1 using a table scan

• accesses t2 using index t2(a)

• checks the condition t2.b BETWEEN 1 AND 3

This plan examines all rows of both tables and performs 100 index look-ups.

With histograms available, the optimizer can choose the following, more efficient plan:

• accesses table t2 in a table scan

• checks the condition t2.b BETWEEN 1 AND 3

• accesses t1 using index t1(a)

This plan also examine all rows from t2, but it performs only 10 look-ups to access 10 rows of table t1.

System Variables

There are a number of system variables that affect histograms.

histogram_size

The histogram_size variable determines the size, in bytes, from 0 to 255, used for a histogram. This is effectively the number of bins for histogram_type=SINGLE_PREC_HB or number of bins/2 for histogram_type=DOUBLE_PREC_HB. If it is set to 0 (the default for MariaDB 10.4.2 and below), no histograms are created when running an ANALYZE TABLE.

histogram_type

The histogram_type variable determines whether single precision (SINGLE_PREC_HB) or double precision (DOUBLE_PREC_HB) height-balanced histograms are created. From MariaDB 10.4.3, double precision is the default. For MariaDB 10.4.2 and below, single precision is the default.

From MariaDB 10.8, JSON_HB, JSON-format histograms, are accepted.

optimizer_use_condition_selectivity

The optimizer_use_condition_selectivity controls which statistics can be used by the optimizer when looking for the best query execution plan.

• 1 Use selectivity of predicates as in MariaDB 5.5.

• 2 Use selectivity of all range predicates supported by indexes.

• 3 Use selectivity of all range predicates estimated without histogram.

• 4 Use selectivity of all range predicates estimated with histogram.

• 5 Additionally use selectivity of certain non-range predicates calculated on record sample.

From MariaDB 10.4.1, the default is 4. Until MariaDB 10.4.0, the default is 1.

Example

Here is an example of the dramatic impact histogram-based statistics can make. The query is based on DBT3 Benchmark Q20 with 60 millions records in the lineitem table.

SELECT SQL_CALC_FOUND_ROWS s_name, s_address FROM 
supplier, nation WHERE 
  s_suppkey IN
    (SELECT ps_suppkey FROM partsupp WHERE
      ps_partkey IN (SELECT p_partkey FROM part WHERE 
         p_name LIKE 'forest%') AND 
    ps_availqty > 
      (SELECT 0.5 * SUM(l_quantity) FROM lineitem WHERE
        l_partkey = ps_partkey AND l_suppkey = ps_suppkey AND
        l_shipdate >= DATE('1994-01-01') AND
        l_shipdate < DATE('1994-01-01') + INTERVAL '1' YEAR ))
  AND s_nationkey = n_nationkey
  AND n_name = 'CANADA'
  ORDER BY s_name
  LIMIT 10;

First,

SET optimizer_switch='materialization=off,semijoin=off';

+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows | filt | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | nation   | ALL   |...| 25   |100.00 | Using where;...
| 1 | PRIMARY | supplier | ref   |...| 1447 |100.00 | Using where; Subq
| 2 | DEP SUBQ| partsupp | idxsq |...| 38   |100.00 | Using where
| 4 | DEP SUBQ| lineitem | ref   |...| 3    |100.00 | Using where
| 3 | DEP SUBQ| part     | unqsb |...| 1    |100.00 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(51.78 sec)

Next, a really bad plan, yet one sometimes chosen:

+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows | filt | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | supplier | ALL   |...|100381|100.00 | Using where; Subq
| 1 | PRIMARY | nation   | ref   |...| 1    |100.00 | Using where
| 2 | DEP SUBQ| partsupp | idxsq |...| 38   |100.00 | Using where
| 4 | DEP SUBQ| lineitem | ref   |...| 3    |100.00 | Using where
| 3 | DEP SUBQ| part     | unqsb |...| 1    |100.00 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(7 min 33.42 sec)

Persistent statistics don't improve matters:

SET use_stat_tables='preferably';
+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows | filt | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | supplier | ALL   |...|10000 |100.00 | Using where;
| 1 | PRIMARY | nation   | ref   |...| 1    |100.00 | Using where
| 2 | DEP SUBQ| partsupp | idxsq |...| 80   |100.00 | Using where
| 4 | DEP SUBQ| lineitem | ref   |...| 7    |100.00 | Using where
| 3 | DEP SUBQ| part     | unqsb |...| 1    |100.00 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(7 min 40.44 sec)

The default flags for optimizer_switch do not help much:

SET optimizer_switch='materialization=DEFAULT,semijoin=DEFAULT';
+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows  | filt  | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | supplier | ALL   |...|10000  |100.00 | Using where;
| 1 | PRIMARY | nation   | ref   |...| 1     |100.00 | Using where
| 1 | PRIMARY | <subq2>  | eq_ref|...| 1     |100.00 |
| 2 | MATER   | part     | ALL   |.. |2000000|100.00 | Using where
| 2 | MATER   | partsupp | ref   |...| 4     |100.00 | Using where; Subq
| 4 | DEP SUBQ| lineitem | ref   |...| 7     |100.00 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(5 min 21.44 sec)

Using statistics doesn't help either:

SET optimizer_switch='materialization=DEFAULT,semijoin=DEFAULT';
SET optimizer_use_condition_selectivity=4;

+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows  | filt  | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | nation   | ALL   |...| 25    |4.00   | Using where
| 1 | PRIMARY | supplier | ref   |...| 4000  |100.00 | Using where;
| 1 | PRIMARY | <subq2>  | eq_ref|...| 1     |100.00 |
| 2 | MATER   | part     | ALL   |.. |2000000|1.56   | Using where
| 2 | MATER   | partsupp | ref   |...| 4     |100.00 | Using where; Subq
| 4 | DEP SUBQ| lineitem | ref   |...| 7     | 30.72 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(5 min 22.41 sec)

Now, taking into account the cost of the dependent subquery:

SET optimizer_switch='materialization=DEFAULT,semijoin=DEFAULT';
SET optimizer_use_condition_selectivity=4;
SET optimizer_switch='expensive_pred_static_pushdown=ON';
+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows | filt  | Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | nation   | ALL   |...| 25   | 4.00  | Using where
| 1 | PRIMARY | supplier | ref   |...| 4000 |100.00 | Using where;
| 2 | PRIMARY | partsupp | ref   |...| 80   |100.00 |
| 2 | PRIMARY | part     | eq_ref|...| 1    | 1.56  | where; Subq; FM
| 4 | DEP SUBQ| lineitem | ref   |...| 7    | 30.72 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(49.89 sec)

Finally, using join_buffer as well:

SET optimizer_switch= 'materialization=DEFAULT,semijoin=DEFAULT';
SET optimizer_use_condition_selectivity=4;
SET optimizer_switch='expensive_pred_static_pushdown=ON';
SET join_cache_level=6;
SET optimizer_switch='mrr=ON';
SET optimizer_switch='mrr_sort_keys=ON';
SET join_buffer_size=1024*1024*16;
SET join_buffer_space_limit=1024*1024*32;
+---+-------- +----------+-------+...+------+----------+------------
| id| sel_type| table    | type  |...| rows | filt |  Extra
+---+-------- +----------+-------+...+------+----------+------------
| 1 | PRIMARY | nation   | AL  L |...| 25   | 4.00  | Using where
| 1 | PRIMARY | supplier | ref   |...| 4000 |100.00 | where; BKA
| 2 | PRIMARY | partsupp | ref   |...| 80   |100.00 | BKA
| 2 | PRIMARY | part     | eq_ref|...| 1    | 1.56  | where Sq; FM; BKA
| 4 | DEP SUBQ| lineitem | ref   |...| 7    | 30.72 | Using where
+---+-------- +----------+-------+...+------+----------+------------

10 ROWS IN SET
(35.71 sec)

See Also

• DECODE_HISTOGRAM()

• Index Statistics

• InnoDB Persistent Statistics

• Engine-independent Statistics

• JSON Histograms (mariadb.org blog)

• Improved histograms in MariaDB 10.8 - Sergei Petrunia - FOSDEM 2022 (video)

• Improving MariaDB’s optimizer with better selectivity estimates - Sergey Petrunia - Server Fest 2021 (video)

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