MySQL - Recursing a tree structure

There's a good-looking article over at mysql.com outlining various ways of managing hierarchical data. I think it provides a full solution to your question, and shows various less simple, but faster approaches (e.g. Nested Sets).

This is an old question, but since i stumbled over this searching for a solution.

Since MySQL 8.0, you can use a recursive CTE for this:

WITH RECURSIVE tmp (id) AS
(
  SELECT id
    FROM locations
    WHERE parent_id IS NULL
  UNION ALL
  SELECT l.id
    FROM tmp AS p JOIN locations AS l
      ON p.id = l.parent_id
)
SELECT * FROM tmp
ORDER BY id;

This assumes a slightly different DB structure than in the original question (eg. there is only one table containing both parents/children), however, I am sure that this technique applies there as well.