  In this paper, we present an algorithm that enumerates a certain class of
signed permutations, referred to as grid signed permutation classes. In the
case of permutations, the corresponding grid classes are of interest because
they are equivalent to the permutation classes that can be enumerated by
polynomials. Furthermore, we apply our results to genome rearrangements and
establish that the number of signed permutations with fixed prefix reversal and
reversal distance is given by polynomials that can be computed by our
algorithm.
