Slow query when joining wp_posts with a lookup-table?

Question

I'm developing a map-based website and need to get posts associated with a place.

Each place has a post in wp_posts and the other associated posts (images of each place etc) is associated with the place using the custom lookup-table wp_lookup_places by post_id.

How can I query to get the results in ms? I thought it would be a simple task for a mysql to filter based on indexed integers?

Rows in lookup: 774 202 Total posts in db: 1 073 777

Current execution time: approx 33 sec

My lookup table:

CREATE TABLE wp_lookup_places (
    post_id bigint(20),
    place_id bigint(20),
    PRIMARY KEY (post_id, place_id)
);

Query from extending WP_Query with a posts_where filter for place with post_id 638891.

SELECT   wp_posts.ID 
FROM wp_posts 
INNER JOIN wp_lookup_places ON  (wp_lookup_places.post_id = wp_posts.ID AND wp_lookup_places.place_id = 638891)  
WHERE 1=1  
AND (wp_posts.post_status = 'publish' OR wp_posts.post_status = 'private') 
ORDER BY wp_posts.post_title ASC LIMIT 0, 250;

Above query with EXPLAIN:

******************** 1. row *********************
           id: 1
  select_type: SIMPLE
        table: wp_posts
         type: ref
possible_keys: PRIMARY,type_status_date
          key: type_status_date
      key_len: 62
          ref: const
         rows: 532062
        Extra: Using index condition; Using where; Using filesort
******************** 2. row *********************
           id: 1
  select_type: SIMPLE
        table: wp_bb_places
         type: eq_ref
possible_keys: PRIMARY
          key: PRIMARY
      key_len: 16
          ref: server01.wp_posts.ID,const
         rows: 1
        Extra: Using where; Using index

Answer 1

It's the order of your primary key declaration. If you're always searching on place_id, declare that first, then post_id:

PRIMARY KEY (place_id, post_id)