¿Cómo convierto una jerarquía relacional en una tabla de cierre en MySQL?

Este es un script antiguo que completé hace 6-7 años para realizar esta tarea en PHP/Propel. Esperemos que sea útil para alguien más:

require_once 'common/Autoloader.php';
require_once 'propel/Propel.php';
\Propel::init('db/runtime-conf.php');

function truncateHierarchy(\PropelPDO $propel) {
    /* @var $state \PropelStatement */
    $state = $propel->prepare('TRUNCATE database.person_hierarchy');
    $state->execute();
}

function insertHierarchy(\PropelPDO $propel, $length) {
    if ($length == 0) {
        $state = $propel->prepare('INSERT INTO database.person_hierarchy SELECT id, id, 0 FROM person;');
        $state->execute();
        return $state->rowCount();
    } else if ($length == 1) {
        $state = $propel->prepare('INSERT INTO database.person_hierarchy SELECT parent_person_id, id, 1 FROM person WHERE id != parent_person_id;');
        $state->execute();
        return $state->rowCount();
    } else {
        $sql = "INSERT INTO database.person_hierarchy \n";
        $sql .= "SELECT p.parent_person_id, c" . ($length - 1) . ".id, " . $length . " FROM database.person AS p \n";
        for ($i = 1; $i <= $length - 1; $i++) {
            $sql .= "LEFT JOIN person AS c" . $i . " ON " . ($i == 1 ? 'p.id' : 'c' . ($i - 1) . '.id') . " = c" . $i . ".parent_person_id \n";
        }
        $sql .= "WHERE p.parent_person_id != p.id \n";
        for ($i = 1; $i <= $length - 1; $i++) {
            $sql .= "AND c" . $i . ".parent_person_id != c" . $i . ".id \n";
        }
        echo $sql;
        $state = $propel->prepare($sql);
        $state->execute();
        return $state->rowCount();
    }
}

/* @var $connect \PropelConnection */
$propel = \Propel::getConnection();
$propel->beginTransaction();

try {
    truncateHierarchy($propel);
    $propel->commit();
} catch (\Exception $e) {
    error_log_exc($e);
    echo "Failed to truncate person hierarchy!\n";
    $propel->rollBack();
    exit();
}

$length = 0;
$inserts = -1;
while ($inserts !== 0 || $length != 10) {
    $propel->beginTransaction();
    try {
        $inserts = insertHierarchy($propel, $length);
        if ($inserts == 0) { 
            echo "No persons exist at length " . $length . ".\n";
        } else {
            echo $inserts . " rows inserted for length " . $length . ".\n";
        }
        $length++;
        $propel->commit();
    } catch (\Exception $e) {
        error_log_exc($e);
        echo "Failed to regenerate person hierarchy!\n";
        $propel->rollBack();
        exit();
    }
}

echo "Regenerated person hierarchy!\n";
exit();