delete post link (wp-admin disabled)

I want users to be able to delete their posts directly on the front-end.
I found several solutions for this, like:
http://www.web-templates.nu/2008/08/25/delete-post-link/

The problem is that i denied the users access to wp-admin. The above solution uses a function located in wp-admin.

Is there another way to do this, or do the users need access to wp-admin to delete their post?