  Kirillov and Reshetikhin conjectured what is now known as the fermionic
formula for the decomposition of tensor products of certain finite dimensional
modules over quantum affine algebras. This formula can also be extended to the
case of $q$-deformations of tensor product multiplicities as recently
conjectured by Hatayama et al. (math.QA/9812022 and math.QA/0102113). In its
original formulation it is difficult to compute the fermionic formula
efficiently. Kleber (q-alg/9611032 and math.QA/9809087) found an algorithm for
the simply-laced algebras which overcomes this problem. We present a method
which reduces all other cases to the simply-laced case using embeddings of
affine algebras. This is the fermionic analogue of the virtual crystal
construction by the authors, which is the realization of crystal graphs for
arbitrary quantum affine algebras in terms of those of simply-laced type.
