  We study Auslander-Reiten components of an artin algebra with bounded short
cycles, namely, there exists a bound for the depths of maps appearing on short
cycles of non-zero non-invertible maps between modules in the given component.
First, we give a number of combinatorial characteri\-zations of almost acyclic
Auslander-Reiten components. Then, we show that an Auslander-Reiten component
with bounded short cycles is closely related to the connec\-ting component of a
tilted quotient algebra. In particular, the number of such components is finite
and each of them is almost acyclic with only finitely many DTr-orbits. As an
application, we show that an artin algebra is representation-finite if and only
if its module category has bounded short cycles. This includes a well known
result of Ringel's, saying that a representation-directed algebra is
representation-finite.
