MYSQL Join/Index optimization - mysql

Question

I have a query that tries to find all shopping carts containing a set of given packages.
For each package I join the corresponding cartitem table once, because I am only interested in carts containing all given packages.
When I reach more than 15 packages(joins) the query performance rapidly drops.
I have two indeces on the corresponding foreign columns and am aware that mysql uses only one of them. When I add an index over the 2 columns(cartitem_package_id,cartitem_cart_id) it works, but is this the only way to solve this situation?
I would like to know why MYSQL suddently stucks in this situation and what may be the mysql internal problem, because I do not see any deeper problem with this definition and query? Does that may be an issue with the query optimizer and can I do something(e.g. adding brackets) to support or force a specific query execution? Or has anyone a different approach here, using another query?
The query looks something like this:
SELECT cart_id
FROM cart
INNER JOIN cartitem as c1 ON cart_id=c1.cartitem_cart_id AND c1.cartitem_package_id= 7
INNER JOIN cartitem as c2 ON cart_id=c2.cartitem_cart_id AND c2.cartitem_package_id= 8
INNER JOIN cartitem as c3 ON cart_id=c3.cartitem_cart_id AND c3.cartitem_package_id= 9
INNER JOIN cartitem as c4 ON cart_id=c4.cartitem_cart_id AND c4.cartitem_package_id= 10
INNER JOIN cartitem as c5 ON cart_id=c5.cartitem_cart_id AND c5.cartitem_package_id= 11
INNER JOIN cartitem as c6 ON cart_id=c6.cartitem_cart_id AND c6.cartitem_package_id= 12
INNER JOIN cartitem as c7 ON cart_id=c7.cartitem_cart_id AND c7.cartitem_package_id= 13
INNER JOIN cartitem as c8 ON cart_id=c8.cartitem_cart_id AND c8.cartitem_package_id= 14
INNER JOIN cartitem as c9 ON cart_id=c9.cartitem_cart_id AND c9.cartitem_package_id= 15
INNER JOIN cartitem as c10 ON cart_id=c10.cartitem_cart_id AND c10.cartitem_package_id= 16
INNER JOIN cartitem as c11 ON cart_id=c11.cartitem_cart_id AND c11.cartitem_package_id= 17
INNER JOIN cartitem as c12 ON cart_id=c12.cartitem_cart_id AND c12.cartitem_package_id= 18
INNER JOIN cartitem as c13 ON cart_id=c13.cartitem_cart_id AND c13.cartitem_package_id= 19
INNER JOIN cartitem as c14 ON cart_id=c14.cartitem_cart_id AND c14.cartitem_package_id= 20
INNER JOIN cartitem as c15 ON cart_id=c15.cartitem_cart_id AND c15.cartitem_package_id= 21
INNER JOIN cartitem as c16 ON cart_id=c16.cartitem_cart_id AND c16.cartitem_package_id= 22
INNER JOIN cartitem as c17 ON cart_id=c17.cartitem_cart_id AND c17.cartitem_package_id= 23
Output:
No result.
Consider the following sample structure:
CREATE TABLE IF NOT EXISTS `cart` (
`cart_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`cart_state` smallint(20) DEFAULT NULL,
PRIMARY KEY (`cart_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 AUTO_INCREMENT=80 ;
INSERT INTO `cart` (`cart_id`, `cart_state`) VALUES
(1, 0),(2, 5),(3, 0),(4, 0),(5, 0),(6, 0),(7, 0),(8, 0),(9, 0),(10, 0),(11, 0),(12, 0),(13, 0),(14, 5),(15, 5),(16, 10),(17, 0),(18, 10),(19, 40),(20, 10),(21, 5),(22, 0),(23, 10),(24, 10),(25, 0),(26, 10),(27, 5),(28, 5),(29, 0),(30, 5),(31, 0),(32, 0),(33, 0),(34, 0),(35, 0),(36, 0),(37, 0),(38, 0),(39, 0),(40, 0),(41, 0),(42, 0),(43, 0),(44, 0),(45, 40),(46, 0),(47, 0),(48, 1),(49, 0),(50, 5),(51, 0),(52, 0),(53, 5),(54, 5),(55, 0),(56, 0),(57, 10),(58, 0),(59, 0),(60, 5),(61, 0),(62, 0),(63, 10),(64, 0),(65, 5),(66, 5),(67, 10),(68, 10),(69, 0),(70, 0),(71, 10),(72, 0),(73, 10),(74, 0),(75, 10),(76, 0),(77, 10),(78, 0),(79, 10);
CREATE TABLE IF NOT EXISTS `cartitem` (
`cartitem_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`cartitem_package_id` int(10) unsigned DEFAULT NULL,
`cartitem_cart_id` int(10) unsigned DEFAULT NULL,
`cartitem_price` decimal(7,2) NOT NULL DEFAULT '0.00',
PRIMARY KEY (`cartitem_id`),
KEY `cartitem_package_id` (`cartitem_package_id`),
KEY `cartitem_cart_id` (`cartitem_cart_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 AUTO_INCREMENT=89 ;
INSERT INTO `cartitem` (`cartitem_id`, `cartitem_package_id`, `cartitem_cart_id`, `cartitem_price`) VALUES
(1, 4, 2, 200.00),(2, 7, 3, 30.00),(3, 14, 9, 255.00),(4, 14, 9, 255.00),(5, 22, 9, 120.00),(6, 22, 9, 120.00),(7, 13, 13, 300.00),(8, 13, 13, 300.00),(9, 7, 14, 450.00),(10, 13, 14, 250.00),(11, 17, 14, 150.00),(12, 7, 15, 450.00),(13, 13, 15, 250.00),(14, 18, 15, 127.50),(15, 7, 16, 450.00),(16, 17, 16, 150.00),(17, 7, 18, 450.00),(18, 7, 19, 450.00),(19, 17, 19, 150.00),(20, 21, 19, 25.00),(21, 13, 20, 300.00),(22, 7, 21, 550.00),(23, 19, 21, 105.00),(24, 22, 21, 120.00),(25, 17, 22, 150.00),(26, 7, 23, 550.00),(27, 11, 24, 245.00),(31, 7, 26, 450.00),(32, 21, 26, 25.00),(33, 21, 26, 25.00),(34, 22, 26, 120.00),(35, 23, 26, 120.00),(36, 10, 27, 382.50),(37, 22, 27, 120.00),(38, 13, 27, 250.00),(39, 10, 28, 297.50),(43, 7, 29, 550.00),(41, 20, 28, 82.50),(42, 22, 28, 120.00),(44, 7, 30, 550.00),(46, 22, 30, 120.00),(47, 23, 30, 120.00),(48, 21, 18, 25.00),(49, 21, 19, 25.00),(50, 17, 37, 150.00),(51, 17, 37, 150.00),(52, 21, 37, 25.00),(53, 21, 37, 25.00),(54, 4, 45, 1.20),(55, 6, 45, 0.00),(56, 7, 47, 450.00),(57, 4, 50, 200.00),(58, 13, 52, 250.00),(59, 13, 19, 300.00),(60, 9, 19, 0.00),(61, 17, 53, 150.00),(62, 7, 53, 450.00),(63, 22, 18, 120.00),(64, 7, 16, 450.00),(65, 7, 54, 450.00),(66, 7, 57, 450.00),(67, 17, 57, 150.00),(68, 7, 56, 450.00),(69, 17, 59, 150.00),(70, 7, 60, 450.00),(71, 17, 61, 150.00),(72, 17, 63, 150.00),(73, 21, 65, 25.00),(74, 7, 66, 450.00),(75, 7, 67, 450.00),(76, 11, 68, 385.00),(77, 7, 71, 450.00),(78, 11, 73, 385.00),(79, 13, 73, 300.00),(80, 4, 75, 200.00),(82, 7, 73, 30.00),(83, 18, 73, 127.50),(84, 23, 73, 120.00),(85, 7, 73, 30.00),(86, 10, 77, 382.50),(87, 7, 79, 550.00),(88, 17, 79, 150.00);
The given query was a possible edge case leading to no results in this example.
SELECT cart_id
FROM cart
INNER JOIN cartitem as c1 ON cart_id=c1.cartitem_cart_id AND c1.cartitem_package_id= 7
INNER JOIN cartitem as c3 ON cart_id=c3.cartitem_cart_id AND c3.cartitem_package_id= 9
INNER JOIN cartitem as c4 ON cart_id=c4.cartitem_cart_id AND c4.cartitem_package_id= 13
INNER JOIN cartitem as c5 ON cart_id=c5.cartitem_cart_id AND c5.cartitem_package_id= 17
INNER JOIN cartitem as c6 ON cart_id=c6.cartitem_cart_id AND c6.cartitem_package_id= 21
Output:
cart_id
-------------
19
19
The query should return all carts containing items that are connected to packages(7,9,13,17,21) in this case.

Answer 1

My approach to your problem would be:
SELECT
cart_id
FROM
cart
INNER JOIN
cartitem
ON
cart_id = cartitem_cart_id
WHERE
cartitem_package_id IN (7,9,13,17,21) -- items that got to be in the cart
GROUP BY
cart_id
HAVING
count(distinct cartitem_package_id) = 5 -- number of different packages
;
DEMO with your data
Explanation
The principle is to filter first with the list of the desired values, here your packages. Now count the different packages per cart (GROUP BY cart_id). If this count matches the number of values in your filter list, then every single package must be in this cart.
You can replace the value list of the IN clause with a subselect, if you get those values from a subselect.
You should see that this approach should be easy to adapt to similar needs.