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Här är en lösning som verkar fungera:

SELECT t.*, DATEDIFF(t.LatestAvailable, t.EarliestAvailable) AS LengthAvailable
FROM 
   (SELECT u.*,
      COALESCE(b1.End, @StartOfWindow) AS EarliestAvailable,
      COALESCE(b2.Start, @EndOfWindow) AS LatestAvailable
    FROM LettingUnits u
    LEFT OUTER JOIN LettingUnitBookings b1
      ON (u.ID = b1.F_LU_ID AND b1.End BETWEEN @StartOfWindow AND @EndOfWindow)
    LEFT OUTER JOIN LettingUnitBookings b2
      ON (u.ID = b2.F_LU_ID AND b2.Start BETWEEN @StartOfWindow AND @EndOfWindow
          AND b2.Start >= b1.End) -- edit: new term
    ) AS t
LEFT OUTER JOIN LettingUnitBookings x
  ON (t.ID = x.F_LU_ID AND x.Start < t.LatestAvailable AND x.End > t.EarliestAvailable)
WHERE x.ID IS NULL AND DATEDIFF(t.LatestAvailable, t.EarliestAvailable) >= @WindowSize;

Utdata är:

+-----+-------------+-------------------+-----------------+-----------------+
| ID  | Name        | EarliestAvailable | LatestAvailable | LengthAvailable |
+-----+-------------+-------------------+-----------------+-----------------+
| 123 | Foo Cottage | 2009-01-05        | 2009-01-10      |               5 |
| 123 | Foo Cottage | 2009-01-20        | 2009-01-25      |               5 |
| 456 | Bar Cottage | 2009-01-20        | 2009-01-31      |              11 |
+-----+-------------+-------------------+-----------------+-----------------+

Analyserar detta med EXPLAIN visar att den använder index ganska bra:

+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------------------+
| id | select_type | table      | type   | possible_keys | key     | key_len | ref   | rows | Extra                   |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------------------+
|  1 | PRIMARY     | <derived2> | ALL    | NULL          | NULL    | NULL    | NULL  |    9 | Using where             |
|  1 | PRIMARY     | x          | ref    | F_LU_ID       | F_LU_ID | 8       | t.ID  |    2 | Using where; Not exists |
|  2 | DERIVED     | u          | system | NULL          | NULL    | NULL    | NULL  |    1 |                         |
|  2 | DERIVED     | b1         | ref    | F_LU_ID       | F_LU_ID | 8       | const |    0 |                         |
|  2 | DERIVED     | b2         | ref    | F_LU_ID       | F_LU_ID | 8       | const |    0 |                         |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------------------+

Jämför med EXPLAIN rapport för lösningen given a> av @martin clayton:

+----+--------------+---------------------+--------+---------------+---------+---------+------+------+---------------------------------+
| id | select_type  | table               | type   | possible_keys | key     | key_len | ref  | rows | Extra                           |
+----+--------------+---------------------+--------+---------------+---------+---------+------+------+---------------------------------+
|  1 | PRIMARY      | lu                  | system | PRIMARY,ID    | NULL    | NULL    | NULL |    1 |                                 |
|  1 | PRIMARY      | <derived2>          | ALL    | NULL          | NULL    | NULL    | NULL |    4 | Using where                     |
|  2 | DERIVED      | <derived3>          | ALL    | NULL          | NULL    | NULL    | NULL |    4 | Using temporary; Using filesort |
|  2 | DERIVED      | <derived5>          | ALL    | NULL          | NULL    | NULL    | NULL |    4 | Using where; Using join buffer  |
|  5 | DERIVED      | LettingUnitBookings | ALL    | NULL          | NULL    | NULL    | NULL |    3 |                                 |
|  6 | UNION        | LettingUnitBookings | index  | NULL          | F_LU_ID | 8       | NULL |    3 | Using index                     |
| NULL | UNION RESULT | <union5,6>          | ALL    | NULL          | NULL    | NULL    | NULL | NULL |                                 |
|  3 | DERIVED      | LettingUnitBookings | ALL    | NULL          | NULL    | NULL    | NULL |    3 |                                 |
|  4 | UNION        | LettingUnitBookings | index  | NULL          | F_LU_ID | 8       | NULL |    3 | Using index                     |
| NULL | UNION RESULT | <union3,4>          | ALL    | NULL          | NULL    | NULL    | NULL | NULL |                                 |
+----+--------------+---------------------+--------+---------------+---------+---------+------+------+---------------------------------+

I allmänhet vill du undvika optimeringsplaner som tvingar fram Using filesort eller Using temporary eftersom dessa är prestationsdödare. En fråga som använder GROUP BY är nästan säker på att orsaka denna typ av optimering, åtminstone i MySQL.