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. It is probably slower than apt-get’s default solver but if you run into conflicts, aspcud will find a solution (if there is one). All you have to do is install and then select aspcud as solver:

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.