# Histogram-based Statistics

Histograms were introduced in MariaDB 10.0.2

### Contents

Histogram-based statistics were introduced in MariaDB 10.0.2 as a mechanism to improve the query plan chosen by the optimizer in certain situations. Until then, 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.

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), 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. Single precision is the default.

### 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.

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
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)
```