Optimizing ORDER BY from joined column - postgresql

Question

I have a display that lists each user in a city and their last message in a table sorted by the newest messages first:
Users
------
Caleb - Hey what's up?
------
Bill - Is there anything up tonight?
------
Jon - What's up man?
------
Any help optimizing this query below and/or helping figure out where to add indexes would be very helpful.
I could probably denormalize and store last_message_created_at on users but want to avoid that backfill.
Users Table:
Table "public.users"
Column | Type | Modifiers
-------------------+-----------------------------+-----------
id | integer | not null
role | user_role | not null
last_message_id | integer |
city_id | integer |
Indexes:
"users_pkey" PRIMARY KEY, btree (id)
"ix_users_city_id" btree (city_id)
"ix_users_last_message_id" btree (last_message_id)
Foreign-key constraints:
"messages_last_message_id_fkey" FOREIGN KEY (last_message_id) REFERENCES messages(id)
"users_city_id_fkey" FOREIGN KEY (city_id) REFERENCES cities(id)
Referenced by:
TABLE "messages" CONSTRAINT "messages_from_user_id_fkey" FOREIGN KEY (from_user_id) REFERENCES users(id)
TABLE "messages" CONSTRAINT "messages_to_user_id_fkey" FOREIGN KEY (to_user_id) REFERENCES users(id)
Messages Table:
Table "public.messages"
Column | Type | Modifiers
------------------+-----------------------------+-------------------------------------------------------
id | integer | not null default nextval('messages_id_seq'::regclass)
content | character varying |
from_user_id | integer |
to_user_id | integer |
created_at | timestamp without time zone |
Indexes:
"messages_pkey" PRIMARY KEY, btree (id)
"ix_messages_from_user_id" btree (from_user_id)
"ix_messages_to_user_id" btree (to_user_id)
Foreign-key constraints:
"messages_from_user_id_fkey" FOREIGN KEY (from_user_id) REFERENCES users(id)
"messages_to_user_id_fkey" FOREIGN KEY (to_user_id) REFERENCES users(id)
Referenced by:
TABLE "users" CONSTRAINT "messages_last_message_id_fkey" FOREIGN KEY (last_message_id) REFERENCES messages(id)
Query and Plan:
EXPLAIN ANALYZE
SELECT users.city_id AS users_city_id, users.id AS users_id, users.last_message_id AS users_last_message_id
FROM users
JOIN messages ON messages.id = users.last_message_id
WHERE users.city_id = 1 ORDER BY users.last_message_id DESC;
QUERY PLAN
---------------------------------------------------------------------------------------------------------------------------
Sort (cost=951606.67..951811.07 rows=81760 width=12) (actual time=1934.501..1998.216 rows=79454 loops=1)
Sort Key: users.last_message_id
Sort Method: quicksort Memory: 6797kB
-> Nested Loop (cost=1575.71..944935.41 rows=81760 width=12) (actual time=26.784..1817.478 rows=79454 loops=1)
-> Bitmap Heap Scan on users (cost=1575.71..33209.21 rows=84040 width=12) (actual time=26.656..393.749 rows=85348 loops=1)
Recheck Cond: (city_id = 1)
-> Bitmap Index Scan on ix_users_city_id (cost=0.00..1554.70 rows=84040 width=0) (actual time=20.679..20.679 rows=85348 loops=1)
Index Cond: (city_id = 1)
-> Index Only Scan using messages_pkey on messages (cost=0.00..10.84 rows=1 width=4) (actual time=0.012..0.013 rows=1 loops=85348)
Index Cond: (id = users.last_message_id)
Heap Fetches: 79454
Total runtime: 2058.134 ms
(12 rows)

Answer 1

You never use the messages table in the query for any other purpose than excluding users without messages so this might be faster:
select
u.city_id as users_city_id,
u.id as users_id,
u.last_message_id as users_last_message_id
from users u
where
u.city_id = 1
and exists (
select 1
from messages
where id = u.last_message_id
)
order by u.last_message_id desc