Fix PostgreSQL sometimes using table scans for event_search (#14409)

PostgreSQL may underestimate the number of distinct `room_id`s in
`event_search`, which can cause it to use table scans for queries for
multiple rooms.

Fix this by setting `n_distinct` on the column.

Resolves #14402.

Signed-off-by: Sean Quah <seanq@matrix.org>

changelog.d/14409.bugfix

@@ -0,0 +1 @@
+Fix PostgreSQL sometimes using table scans for queries against the `event_search` table, taking a long time and a large amount of IO.

synapse/storage/schema/main/delta/73/11event_search_room_id_n_distinct.sql.postgres

@@ -0,0 +1,33 @@
+/* Copyright 2022 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
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+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
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+
+
+-- By default the postgres statistics collector massively underestimates the
+-- number of distinct rooms in `event_search`, which can cause postgres to use
+-- table scans for queries for multiple rooms.
+--
+-- To work around this we can manually tell postgres the number of distinct rooms
+-- by setting `n_distinct` (a negative value here is the number of distinct values
+-- divided by the number of rows, so -0.01 means on average there are 100 rows per
+-- distinct value). We don't need a particularly accurate number here, as a) we just
+-- want it to always use index scans and b) our estimate is going to be better than the
+-- one made by the statistics collector.
+
+ALTER TABLE event_search ALTER COLUMN room_id SET (n_distinct = -0.01);
+
+-- Ideally we'd do an `ANALYZE event_search (room_id)` here so that
+-- the above gets picked up immediately, but that can take a bit of time so we
+-- rely on the autovacuum eventually getting run and doing that in the
+-- background for us.