13:50

### The Multi-Column Index of the Mysteries

The one thing that everyone knows about compositive indexes is: If you have an index on (A, B, C), it can’t be used for queries on (B) or (B, C) or (C), just (A), (A, B) or (A, B, C), right? I’ve said that multiple times in talks. It’s clearly true, right?

Well, no, it’s not. It’s one of those things that is not technically true, but it is still good advice.

The documentation on multi-column indexes is pretty clear:

A multicolumn B-tree index can be used with query conditions that involve any subset of the index’s columns, but the index is most efficient when there are constraints on the leading (leftmost) columns. The exact rule is that equality constraints on leading columns, plus any inequality constraints on the first column that does not have an equality constraint, will be used to limit the portion of the index that is scanned.

Let’s try this out!

First, create a table and index:

```
xof=# CREATE TABLE x (
xof(# i integer,
xof(# f float,
xof(# g float
xof(# );
CREATE TABLE
xof=# CREATE INDEX ON x(i, f, g);
CREATE INDEX
```

And fill it with some test data:

```
xof=# INSERT INTO x SELECT 1, random(), random() FROM generate_series(1, 10000000);
INSERT 0 10000000
xof=# INSERT INTO x SELECT 2, random(), random() FROM generate_series(1, 10000000);
INSERT 0 10000000
xof=# INSERT INTO x SELECT 3, random(), random() FROM generate_series(1, 10000000);
INSERT 0 10000000
xof=# ANALYZE x;
ANALYZE
```

And away we go!

```
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
------------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=599859.50..599859.51 rows=1 width=8) (actual time=91876.057..91876.057 rows=1 loops=1)
-> Index Only Scan using x_i_f_g_idx on x (cost=0.56..599097.71 rows=304716 width=8) (actual time=1820.699..91652.409 rows=300183 loops=1)
Index Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Heap Fetches: 300183
Planning time: 3.384 ms
Execution time: 91876.165 ms
(6 rows)
```

And sure enough, it uses the index, even though we didn’t include column `i`

in the query. In this case, the planner thinks that this will be more efficient than just doing a sequential scan on the whole table, even though it has to walk the whole index.

Is it right? Let’s turn off index scans and find out.

```
xof=# SET enable_indexonlyscan = 'off';
SET
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=599859.50..599859.51 rows=1 width=8) (actual time=39691.081..39691.081 rows=1 loops=1)
-> Index Scan using x_i_f_g_idx on x (cost=0.56..599097.71 rows=304716 width=8) (actual time=1820.676..39624.144 rows=300183 loops=1)
Index Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Planning time: 0.181 ms
Execution time: 39691.128 ms
(5 rows)
```

PostgreSQL, you’re not helping!

```
xof=# SET enable_indexscan = 'off';
SET
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=689299.60..689299.61 rows=1 width=8) (actual time=40593.427..40593.428 rows=1 loops=1)
-> Bitmap Heap Scan on x (cost=513444.70..688537.81 rows=304716 width=8) (actual time=37901.773..40542.900 rows=300183 loops=1)
Recheck Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Rows Removed by Index Recheck: 8269763
Heap Blocks: exact=98341 lossy=53355
-> Bitmap Index Scan on x_i_f_g_idx (cost=0.00..513368.52 rows=304716 width=0) (actual time=37860.366..37860.366 rows=300183 loops=1)
Index Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Planning time: 0.160 ms
Execution time: 40593.764 ms
(9 rows)
```

Ugh, *fine*!

```
xof=# SET enable_bitmapscan='off';
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
--------------------------------------------------------------------------------------------------------------------
Aggregate (cost=641836.33..641836.34 rows=1 width=8) (actual time=27270.666..27270.666 rows=1 loops=1)
-> Seq Scan on x (cost=0.00..641074.54 rows=304716 width=8) (actual time=0.081..27195.552 rows=300183 loops=1)
Filter: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Rows Removed by Filter: 29699817
Planning time: 0.157 ms
Execution time: 27270.726 ms
(6 rows)
```

It turns out the seq scan is faster, which isn’t that much of a surprise. Of course, what’s *really* fast is using the index properly:

```
xof=# // reset all query planner settings
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE i IN (1, 2, 3) AND f BETWEEN 0.11 AND 0.12;
QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=92459.82..92459.83 rows=1 width=8) (actual time=6283.162..6283.162 rows=1 loops=1)
-> Index Only Scan using x_i_f_g_idx on x (cost=0.56..91698.03 rows=304716 width=8) (actual time=1.295..6198.409 rows=300183 loops=1)
Index Cond: ((i = ANY ('{1,2,3}'::integer[])) AND (f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Heap Fetches: 300183
Planning time: 1.264 ms
Execution time: 6283.567 ms
(6 rows)
```

And, of course, a dedicated index for that particular operation is the fastest of all:

```
xof=# CREATE INDEX ON x(f);
CREATE INDEX
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
---------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=188492.00..188492.01 rows=1 width=8) (actual time=5536.940..5536.940 rows=1 loops=1)
-> Bitmap Heap Scan on x (cost=4404.99..187662.16 rows=331934 width=8) (actual time=209.854..5466.633 rows=300183 loops=1)
Recheck Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Rows Removed by Index Recheck: 8258716
Heap Blocks: exact=98337 lossy=53359
-> Bitmap Index Scan on x_f_idx (cost=0.00..4322.00 rows=331934 width=0) (actual time=163.402..163.402 rows=300183 loops=1)
Index Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Planning time: 5.586 ms
Execution time: 5537.235 ms
(9 rows)
```

Although, interestingly enough, PostgreSQL doesn’t quite get it right here:

```
xof=# SET enable_bitmapscan='off';
SET
xof=# EXPLAIN ANALYZE SELECT SUM(g) FROM x WHERE f BETWEEN 0.11 AND 0.12;
QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=203875.29..203875.30 rows=1 width=8) (actual time=2178.215..2178.216 rows=1 loops=1)
-> Index Scan using x_f_idx on x (cost=0.56..203045.45 rows=331934 width=8) (actual time=0.161..2110.903 rows=300183 loops=1)
Index Cond: ((f >= '0.11'::double precision) AND (f <= '0.12'::double precision))
Planning time: 0.170 ms
Execution time: 2178.279 ms
(5 rows)
```

So, we conclude:

- Yes, PostgreSQL will sometimes use the second and further columns of a multi-column index, even if the first column isn’t used in the query.
- This is rarely optimal, so it should not be relied on as an optimization path.
- So, while the advice was not correct in the absolute statement, it was still valid as advice.

And there we are.

```
xof=# DROP TABLE x;
DROP TABLE
```