The following PHP worked for me (using mysqli extension but queries should be the same for other extensions):
$db = new mysqli( 'localhost', 'user', 'pass', 'dbname' );
// to get the max_allowed_packet
$maxp = $db->query( 'SELECT @@global.max_allowed_packet' )->fetch_array();
echo $maxp[ 0 ];
// to set the max_allowed_packet to 500MB
$db->query( 'SET @@global.max_allowed_packet = ' . 500 * 1024 * 1024 );
So if you've got a query you expect to be pretty long, you can make sure that mysql will accept it with something like:
$sql = "some really long sql query...";
$db->query( 'SET @@global.max_allowed_packet = ' . strlen( $sql ) + 1024 );
$db->query( $sql );
Notice that I added on an extra 1024 bytes to the length of the string because according to the manual,
The value should be a multiple of 1024; nonmultiples are rounded down to the nearest multiple.
That should hopefully set the max_allowed_packet size large enough to handle your query. I haven't tried this on a shared host, so the same caveat as @Glebushka applies.