  In this article we obtain lower and upper bounds for global dimensions of a
class of artinian algebras in terms of global dimensions of a finite subset of
their artinian subalgebras. Finding these bounds for the global dimension of an
artinian algebra $A$ is realized via an explicit algorithm we develop. This
algorithm is based on a directed graph (not the Auslander-Reiten quiver) we
construct, and it allows us to decide whether an artinian algebra has finite
global dimension in good number of cases.
