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<?php

$getAllIdOfRootCategory = function($catname) {
    $rootCategoryObj = Mage::getModel('catalog/category')->loadByAttribute('name', $catname);
    $collection = Mage::getModel('catalog/category')
        ->getCollection()
        ->addPathsFilter($rootCategoryObj->getPath().'/');

    $arr = array();
    foreach($collection as $catObj) {
        $arr[] = $catObj->getId();
    }

    return implode(",", $arr);
};
//echo $getAllIdOfRootCategory('AcerEMEA Root');