  We develop a fast algorithm for computing the bound of an Ore polynomial over
a skew field, under mild conditions. As an application, we state a criterion
for deciding whether a bounded Ore polynomial is irreducible, and we discuss a
factorization algorithm. The asymptotic time complexity in the degree of the
given Ore polynomial is studied. In the class of Ore polynomials over a finite
field, our algorithm is an alternative to Giesbretch's one that reduces the
complexity in the degree of the polynomial.
