階層配列リストからツリー構造を効率的に構築するにはどうすればよいですか?

$arr = array(
  array('id' => 100, 'parentid' => 0, 'name' => 'a'),
  array('id' => 101, 'parentid' => 100, 'name' => 'a'),
  array('id' => 102, 'parentid' => 101, 'name' => 'a'),
  array('id' => 103, 'parentid' => 101, 'name' => 'a'),
);

$new = array();
foreach ($arr as $a) {
    $new[$a['parentid']][] = $a;
}
$tree = createTree($new, array($arr[0]));
print_r($tree);

function createTree(&$list, $parent){
    $tree = array();
    foreach ($parent as $k => $l){
        if(isset($list[$l['id']])){
            $l['children'] = createTree($list, $list[$l['id']]);
        }
        $tree[] = $l;
    } 
    return $tree;
}