Partitioned table query still scanning all partitions

Question

I have a table with over a billion records. In order to improve performance, I partitioned it to 30 partitions. The most frequent queries have (id = ...) in their where clause, so I decided to partition the table on the id column.

Basically, the partitions were created in this way:

CREATE TABLE foo_0 (CHECK (id % 30 = 0)) INHERITS (foo);
CREATE TABLE foo_1 (CHECK (id % 30 = 1)) INHERITS (foo);
CREATE TABLE foo_2 (CHECK (id % 30 = 2)) INHERITS (foo);
CREATE TABLE foo_3 (CHECK (id % 30 = 3)) INHERITS (foo);
.
.
.

I ran ANALYZE for the entire database and in particular, I made it collect extra statistics for this table's id column by running:

ALTER TABLE foo ALTER COLUMN id SET STATISTICS 10000;

However when I run queries that filter on the id column the planner shows that it's still scanning all the partitions. constraint_exclusion is set to partition, so that's not the problem.

EXPLAIN ANALYZE SELECT * FROM foo WHERE (id = 2);


                                               QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------------------
 Result  (cost=0.00..8106617.40 rows=3620981 width=54) (actual time=30.544..215.540 rows=171477 loops=1)
   ->  Append  (cost=0.00..8106617.40 rows=3620981 width=54) (actual time=30.539..106.446 rows=171477 loops=1)
         ->  Seq Scan on foo  (cost=0.00..0.00 rows=1 width=203) (actual time=0.002..0.002 rows=0 loops=1)
               Filter: (id = 2)
         ->  Bitmap Heap Scan on foo_0 foo  (cost=3293.44..281055.75 rows=122479 width=52) (actual time=0.020..0.020 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_0_idx_1  (cost=0.00..3262.82 rows=122479 width=0) (actual time=0.018..0.018 rows=0 loops=1)
                     Index Cond: (id = 2)
         ->  Bitmap Heap Scan on foo_1 foo  (cost=3312.59..274769.09 rows=122968 width=56) (actual time=0.012..0.012 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_1_idx_1  (cost=0.00..3281.85 rows=122968 width=0) (actual time=0.010..0.010 rows=0 loops=1)
                     Index Cond: (id = 2)
         ->  Bitmap Heap Scan on foo_2 foo  (cost=3280.30..272541.10 rows=121903 width=56) (actual time=30.504..77.033 rows=171477 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_2_idx_1  (cost=0.00..3249.82 rows=121903 width=0) (actual time=29.825..29.825 rows=171477 loops=1)
                     Index Cond: (id = 2)
.
.
.

What could I do to make the planer have a better plan? Do I need to run ALTER TABLE foo ALTER COLUMN id SET STATISTICS 10000; for all the partitions as well?

EDIT

After using Erwin's suggested change to the query, the planner only scans the correct partition, however the execution time is actually worse then a full scan (at least of the index).

EXPLAIN ANALYZE select * from foo where (id % 30 = 2) and (id = 2);
                                                                         QUERY PLAN
                                                                             QUERY PLAN
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Result  (cost=0.00..8106617.40 rows=3620981 width=54) (actual time=32.611..224.934 rows=171477 loops=1)
   ->  Append  (cost=0.00..8106617.40 rows=3620981 width=54) (actual time=32.606..116.565 rows=171477 loops=1)
         ->  Seq Scan on foo  (cost=0.00..0.00 rows=1 width=203) (actual time=0.002..0.002 rows=0 loops=1)
               Filter: (id = 2)
         ->  Bitmap Heap Scan on foo_0 foo  (cost=3293.44..281055.75 rows=122479 width=52) (actual time=0.046..0.046 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_0_idx_1  (cost=0.00..3262.82 rows=122479 width=0) (actual time=0.044..0.044 rows=0 loops=1)
                     Index Cond: (id = 2)
         ->  Bitmap Heap Scan on foo_1 foo  (cost=3312.59..274769.09 rows=122968 width=56) (actual time=0.021..0.021 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_1_idx_1  (cost=0.00..3281.85 rows=122968 width=0) (actual time=0.020..0.020 rows=0 loops=1)
                     Index Cond: (id = 2)
         ->  Bitmap Heap Scan on foo_2 foo  (cost=3280.30..272541.10 rows=121903 width=56) (actual time=32.536..86.730 rows=171477 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_2_idx_1  (cost=0.00..3249.82 rows=121903 width=0) (actual time=31.842..31.842 rows=171477 loops=1)
                     Index Cond: (id = 2)
         ->  Bitmap Heap Scan on foo_3 foo  (cost=3475.87..285574.05 rows=129032 width=52) (actual time=0.035..0.035 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_3_idx_1  (cost=0.00..3443.61 rows=129032 width=0) (actual time=0.031..0.031 rows=0 loops=1)
.
.
.
         ->  Bitmap Heap Scan on foo_29 foo  (cost=3401.84..276569.90 rows=126245 width=56) (actual time=0.019..0.019 rows=0 loops=1)
               Recheck Cond: (id = 2)
               ->  Bitmap Index Scan on foo_29_idx_1  (cost=0.00..3370.28 rows=126245 width=0) (actual time=0.018..0.018 rows=0 loops=1)
                     Index Cond: (id = 2)
 Total runtime: 238.790 ms

Versus:

EXPLAIN ANALYZE select * from foo where (id % 30 = 2) and (id = 2);
                                                                            QUERY PLAN
------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Result  (cost=0.00..273120.30 rows=611 width=56) (actual time=31.519..257.051 rows=171477 loops=1)
   ->  Append  (cost=0.00..273120.30 rows=611 width=56) (actual time=31.516..153.356 rows=171477 loops=1)
         ->  Seq Scan on foo  (cost=0.00..0.00 rows=1 width=203) (actual time=0.002..0.002 rows=0 loops=1)
               Filter: ((id = 2) AND ((id % 30) = 2))
         ->  Bitmap Heap Scan on foo_2 foo  (cost=3249.97..273120.30 rows=610 width=56) (actual time=31.512..124.177 rows=171477 loops=1)
               Recheck Cond: (id = 2)
               Filter: ((id % 30) = 2)
               ->  Bitmap Index Scan on foo_2_idx_1  (cost=0.00..3249.82 rows=121903 width=0) (actual time=30.816..30.816 rows=171477 loops=1)
                     Index Cond: (id = 2)
 Total runtime: 270.384 ms

Answer 1

For non-trivial expressions you have to repeat the more or less verbatim condition in queries to make the Postgres query planner understand it can rely on the CHECK constraint. Even if it seems redundant!

Per documentation:

With constraint exclusion enabled, the planner will examine the constraints of each partition and try to prove that the partition need not be scanned because it could not contain any rows meeting the query's WHERE clause. When the planner can prove this, it excludes the partition from the query plan.

Bold emphasis mine. The planner does not understand complex expressions. Of course, this has to be met, too:

Ensure that the constraint_exclusion configuration parameter is not disabled in postgresql.conf. If it is, queries will not be optimized as desired.

Instead of

SELECT * FROM foo WHERE (id = 2);

Try:

SELECT * FROM foo WHERE id % 30 = 2 AND id = 2;

And:

The default (and recommended) setting of constraint_exclusion is actually neither on nor off, but an intermediate setting called partition, which causes the technique to be applied only to queries that are likely to be working on partitioned tables. The on setting causes the planner to examine CHECK constraints in all queries, even simple ones that are unlikely to benefit.

You can experiment with the constraint_exclusion = on to see if the planner catches on without redundant verbatim condition. But you have to weigh cost and benefit of this setting.

The alternative would be simpler conditions for your partitions as already outlined by @harmic.

An no, increasing the number for STATISTICS will not help in this case. Only the CHECK constraints and your WHERE conditions in the query matter.