Aspcud is a solver for package dependencies. A package universe and a request to install, remove, or upgrade packages have to be encoded in the CUDF format. Such a CUDF document can then be passed to aspcud along with an optimization criteria to obtain a solution to the given package problem.

Aspcud is available as a backend solver for apt-get in debian. More information can be found in the blog entry about using external solvers with apt-get. But if you want to get started quickly:

apt-get install apt-cudf
apt-get -s --solver aspcud install totem

Additional information can be found on aspcud’s home page. And more information about the cudf format can be found on the Mancoosi homepage.