  We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix
product states (MPS). This allows us to treat much larger bath sizes and by
that reach substantially longer times (factor $\sim$ 2 -- 3) than with exact
diagonalization. We show that the star geometry of the underlying impurity
problem can have substantially better entanglement properties than the
previously favoured chain geometry. This has immense consequences for the
efficiency of an MPS-based description of general impurity problems: in the
case of equilibrium DMFT, it leads to an orders-of-magnitude speedup. We
introduce an approximation for the two-time hybridization function that uses
time-translational invariance, which can be observed after a certain relaxation
time after a quench to a time-independent Hamiltonian.
