  We derive an exact mapping from the action of nonequilibrium dynamical
mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with
time-dependent parameters, which can be solved numerically by exact
diagonalization. The representability of the nonequilibrium DMFT action by a
SIAM is established as a rather general property of nonequilibrium Green
functions. We also obtain the nonequilibrium DMFT equations using the cavity
method alone. We show how to numerically obtain the SIAM parameters using
Cholesky or eigenvector matrix decompositions. As an application, we use a
Krylov-based time propagation method to investigate the Hubbard model in which
the hopping is switched on, starting from the atomic limit. Possible future
developments are discussed.
