  Let $\Lambda$ be a finite-dimensional algebra over an algebraically closed
field, then $\Lambda$ is either tame or wild. Is there any homological
description in terms of AR-translations on tameness? Or equivalently, is there
any combinatorial description in terms of AR-quivers? The answer is yes. In the
present paper we prove the following main theorem: ``$\Lambda$ is tame if and
only if almost all modules are isomorphic to their Auslander-Reiten
translations, if and only if they lie in homogeneous tubes".
  The method used in the paper is bimodule problem, which has been studied by
several authors. We treat bimodule problems and their reductions in terms of
matrices and generalized Jordan forms respectively. In particular, we introduce
a concept of freely parameterized bimodule problems corresponding to layered
bocses in order to define the reductions of bimodule problems. Moreover, we
list all the possibilities of the differential of the first arrow of a layered
bocs such that the induced bocs is still layered and preserves all the free
parameters, especially in wild case.
