MySQL polymorphic join condition with OR not using index - mysql

Question

I have tables departments, employees, and emails in MySQL 5.6.17 (for a Rails app). Each department has many employees, and both departments and employees have many emails. I want to sort departments by the number of emails to the entire department and individual employees within the department. My attempt:
SELECT departments.*, COUNT(DISTINCT employees.id) AS employees_count, COUNT(DISTINCT emails.id) AS emails_count
FROM departments
LEFT OUTER JOIN employees
ON employees.department_id = departments.id AND employees.is_employed = true
LEFT OUTER JOIN emails
ON (emails.emailable_id = departments.id AND emails.emailable_type = 'department')
OR (emails.emailable_id = employees.id AND emails.emailable_type = 'employee')
GROUP BY departments.id
ORDER BY emails_count DESC
LIMIT 20;
Unfortunately, this query takes over 3 minutes to complete. Since this query will be used in a web interface, that's not a workable timeframe. An EXPLAIN gives:
+----+-------------+-------------+-------+-------------------------------------------------+----------------------------------+---------+-------------------------------+-------+------------------------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------------+-------+-------------------------------------------------+----------------------------------+---------+-------------------------------+-------+------------------------------------------------+
| 1 | SIMPLE | departments | index | PRIMARY | PRIMARY | 4 | NULL | 37468 | Using where; Using temporary; Using filesort |
| 1 | SIMPLE | employees | ref | index_employees_on_department_id | index_employees_on_department_id | 5 | development_db.departments.id | 5 | Using where |
| 1 | SIMPLE | emails | ALL | index_emails_on_emailable_id_and_emailable_type | NULL | NULL | NULL | 10278 | Range checked for each record (index map: 0x2) |
+----+-------------+-------------+-------+-------------------------------------------------+----------------------------------+---------+-------------------------------+-------+------------------------------------------------+
The index on emails is, then, not being used. This index is used successfully when I join emails only to departments or only to employees, but not with both at once.
Why is this? What can I do about this? Is there a more efficient way to query the desired data?

Answer 1

It might help to do the aggregation first before the joins:
SELECT d.*, e.employees_count, em.emails_count
FROM d LEFT OUTER JOIN
(SELECT e.department_id, count(*) as employees_count
FROM employees e
WHERE e.is_employed = true
GROUP BY e.department_id
) e
ON e.department_id = d.id LEFT OUTER JOIN
(SELECT department_id, count(distinct id) as emails_count
FROM (SELECT em.emailable_id as department_id, em.id
FROM emails em
WHERE em.emailable_type = 'department'
UNION ALL
SELECT e.department_id, em.id
FROM emails em JOIN
employees e
ON em.emailable_id = e.id AND em.emailable_type = 'employee'
) ee
GROUP BY department_id
) em
ON em.department_id = d.id LEFT OUTER JOIN
ORDER BY emails_count DESC
LIMIT 20;
You also want an index on emails(emailable_id, emailable_type, id) and on emails(emailable_type, emailable_id, id).