Slow and memory problems: Refresh category with 100 products

Question

I have a category with 100 new products. After an import I remove all products from this category and add 100 new products. This is very slow and cause memory problems, so I am doing something wrong. Here is the code:

public function removeAllFromNew()
{
    $category_id = 8;
    $products = Mage::getModel('catalog/product')->getCollection()
        ->addCategoryFilter(Mage::getModel('catalog/category')->load($category_id));
    foreach($products as $product)
    {
        $categories = $product->getCategoryIds();
        if(in_array($category_id, $categories))
        {
            $product_load = Mage::getSingleton('catalog/product')->load($product->getId());
            $categories = array_diff($categories, array($category_id));
            $product_load->setCategoryIds( $categories );
            $product_load->save();
        }
    }
}
public function updateNew()
{
    self::removeAllFromNew();

    $category_id = 8;
    $products = Mage::getModel('catalog/product')->getCollection()
        ->addAttributeToFilter('neuheiten', array('neq' => '') )
        ->addAttributeToSort('neuheiten', 'desc')
        ->addStoreFilter()
        ->setPage(0, 100);

    foreach($products as $product)
    {
        $categories = $product->getCategoryIds();
        $categories[] = $category_id;
        $product_load = Mage::getSingleton('catalog/product')->load($product->getId());
        $product_load->setCategoryIds( $categories );
        $product_load->save();
    }
}

How can I do this any better?

I think at first I should not query all products in removeAllFromNew(). How can I limit this to products in a category?

Update I added a addCategoryFilter in removeAllFromNew() but it looks like adding a product to the category is the slow part.