Inefficient Function to pull sub-categories using too many queries?

Hey all. I’ve written a totally useful and effective function that will sort through each of the sub-categories of a specified wordpress category, and list the most recent 10 articles within each sub-category. All is working well, but I fear my code may not be as efficient as it could be. I currently have a master category called “Articles” with four sub-categories, but this function scales as I add more sub-categories. The below function is adding 28 queries to my page…bringing me to a grand total of 69 queries.

Any input would be terrific. Thanks!

<?php
//FUNCTION LOADS ALL SUBCATEGORIES FROM A SPECIFIED CATEGORY AND THEN
//LISTS ARTICLES WITHING THAT CATEGORY IN AN ORDERED LIST

$cat = 1; //manually specify category #1 which happens to be ARTICLES
$displaynum = 10; //specify the # of articles headlines to show in each sub-category

$args=array(
   'orderby' => 'name',
   'order' => 'ASC',
   'title_li' => '',
   'hide_empty' => '0',
   'parent' => $cat
);
$categories=get_categories($args);

//LOOP THROUGH EACH SUBCATEGORY OF #1 ABOVE AND FORMAT IN DIV
$countbox = 1;

foreach($categories as $category) {
echo '<div id="'.$category->slug.'" class="catbox ';
//add right-padding to odd numbered boxes which appear on the left
if( $odd != $countbox%2 ) echo 'leftbox'; else echo 'rightbox';
echo '">';
echo '<h3>'.$category->name.'</h3>';

    //OUTPUT HEADLINES FROM EACH SUBCATEGORY IN A LIST

    query_posts('category_name='.$category->slug.'&showposts='.$displaynum); {
    echo "\n<ul>";
    while (have_posts()) : the_post();
    echo '<li>';
    echo '<a href="';
    the_permalink();
    echo '">';
    the_title();
    echo '</a></li>';
    endwhile;
    echo "</ul>\n";
    }

echo '
<a class="more" href="' . get_category_link( $category->term_id ) . '"
title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>read more</a> ';
echo '</div><!--end '.$category->slug.' div-->';
echo "\n";
$countbox++;

}
?>