  We review three vector encodings of Bayesian network structures. The first
one has recently been applied by Jaakkola 2010, the other two use special
integral vectors formerly introduced, called imsets [Studeny 2005, Studeny
2010]. The central topic is the comparison of outer polyhedral approximations
of the corresponding polytopes. We show how to transform the inequalities
suggested by Jaakkola et al. to the framework of imsets. The result of our
comparison is the observation that the implicit polyhedral approximation of the
standard imset polytope suggested in [Studeny 2011] gives a closer
approximation than the (transformed) explicit polyhedral approximation from
[Jaakkola 2010]. Finally, we confirm a conjecture from [Studeny 2011] that the
above-mentioned implicit polyhedral approximation of the standard imset
polytope is an LP relaxation of the polytope.
