$people = array();
for($i=0; $i < 15; $i++)
{
    $people[] = chr(65 + $i);
}
shuffle($people);

$unmatched = array('AG', 'HJ', 'BF', 'CI');

$rotated_people = $people;
array_push($rotated_people, array_shift($rotated_people));
$queue = array(
    $people,
    $rotated_people,
);

for ($i=0; $i<15; $i++) {
    $give = $queue[0][$i];
    $get = $queue[1][$i];
    if ( ! in_array([$give . $get, $get . $give], $unmatched) && $give != $get )
    {
        echo $give . ' gives present to ' . $get . "<br/>";
    }
}