PostgreSQL – Uniqueness Constraint for Elements of Arrays in Entire Table

You have two conditions to check during the authentication:

1. There is a user with matching username; do not need to match by email.

2. There are no users with matching usernames; need to match by email.

So the query is:

WITH matching_username AS (SELECT * FROM member WHERE username = 'john@domain.com')
SELECT * FROM matching_username WHERE (SELECT COUNT(*) FROM matching_username) = 1
                                   AND pw_hash = 'x1j34'
UNION 
SELECT * FROM member            WHERE (SELECT COUNT(*) FROM matching_username) = 0
                                   AND email = 'john@domain.com' 
                                   AND pw_hash='x1j34';

On the other hand, there is a problem with your design of the table.

What if two users have have the same email, but neither of them have email as their username? If one of them tries to authenticate with an email, you will not be able to tell, which user record to authenticate against.

Exclude users without emails

Assuming we only want users that actually have emails. Users without emails are ignored. The reason I went with this assumption at first is that all your queries do that already:

LEFT JOIN emails on users.id = emails.user_id
WHERE emails.email LIKE 'a' || '%%'

By adding a WHERE condition on emails.email you effectively convert your LEFT JOIN to a plain [INNER] JOIN and exclude users without emails. Detailed explanation:

• Query with LEFT JOIN not returning rows for count of 0

2nd query rewritten

Your 2nd query does not work as advertised, results are not "descending by number of emails". You have to nest the result of count() in another CTE or subquery and run dense_rank() on it. You cannot nest window functions in the same query level.

SELECT u.name, e2.*
FROM  (
   SELECT *, dense_rank() OVER (ORDER BY n_emails, users.id) AS rnk
   FROM  (
      SELECT user_id, id AS e_id, e_mail
           , count(*) OVER (PARTITION BY user_id) AS n_emails          
      FROM   emails
      WHERE  email LIKE 'a' || '%'  -- one % is enough
      ) e1
   ) e2
JOIN   users u ON u.id = e2.user_id
WHERE  rnk < 3
ORDER  BY rnk;

This should be fastest if the predicate is selective enough (selects only a small fraction of all emails). Two window functions with rows sorted differently have their price, too.

• A major point is to run the subquery on emails only - which is possible if the preliminary assumption holds.

3rd query improved

If, on the other hand, the predicate WHERE e.email LIKE 'a' || '%' is not very selective, your 3rd query is probably faster, even if it reads from the table twice - but the second time only desired rows. Also improved:

SELECT e.user_id, u.name,
       e.id AS e_id, e.e_mail, sq.n_emails
FROM  (
   SELECT user_id, count(*) AS n_emails
   FROM   emails
   WHERE  email LIKE 'a' || '%'
   GROUP  BY user_id
   ORDER  BY count(*) DESC, user_id  -- break ties
   LIMIT  2  OFFSET 0
   ) sq
JOIN   emails e USING (user_id)
JOIN   users  u ON u.id = e.user_id
WHERE  e.email LIKE 'a' || '%'
ORDER  BY sq.n_emails DESC;

Include users without emails

You can either include the users table in the inner query again, similar to what you had before. But you have to pull the filter on email into the join condition!

SELECT u.name, e2.*
FROM  (
   SELECT *, dense_rank() OVER (ORDER BY n_emails, users.id) AS rnk
   FROM  (
      SELECT u.id AS user_id, u.name, e.id AS e_id
           , count(e.user_id) OVER (PARTITION BY u.id) AS n_emails          
      FROM   users u
      LEFT   JOIN emails e ON e.user_id = u.id
                          AND e.email LIKE 'a' || '%'  -- !!!
      ) e1
   ) e2
WHERE  rnk < 3
ORDER  BY rnk;

Which will be a bit more expensive.

Since you retrieve users with the most emails first, users without emails will rarely be in the result. To optimize performance, you could use a UNION ALL with LIMIT:

(  -- parentheses required
SELECT u.name, e2.user_id, e2.e_id, e2.e_mail, e2.n_emails
FROM  (
   SELECT *, dense_rank() OVER (ORDER BY n_emails, users.id) AS rnk
   FROM  (
      SELECT user_id, id AS e_id, e_mail
           , count(*) OVER (PARTITION BY user_id) AS n_emails          
      FROM   emails
      WHERE  email LIKE 'a' || '%'  -- one % is enough
      ) e1
   ) e2
JOIN   users u ON u.id = e2.user_id
WHERE  rnk < 3      -- adapt to paging!
ORDER  BY rnk
)
UNION ALL
(    
SELECT u.name, u.user_id, NULL AS e_id, NULL AS e_mail, 0 AS n_emails  
FROM   users       u
LEFT   JOIN emails e ON e.user_id = u.id
                    AND e.email LIKE 'a' || '%'
WHERE  e.e.user_id IS NULL
)
OFFSET 0      -- adapt to paging!
LIMIT  2      -- adapt to paging!

Detailed explanation:

• Optimize a query on two big tables

MATERIALIZED VIEW

I would consider materializing the result for two reasons:

• Subsequent queries are much faster.
• You don't have to operate on a moving target. You speak of paging, and if users get new emails between pages, your whole sort order may be moot.

Build a MV from the 2nd query without LIMIT (REFRESH MATERIALIZED VIEW), then return the first page etc. It's a matter of policy, when you refresh the MV again.