  We demonstrate that the dynamics of an open quantum system can be calculated
efficiently and with predefined error, provided a basis exists in which the
system-environment interactions are local and hence obey the Lieb-Robinson
bound. We show that this assumption can generally be made. Defining a dynamical
renormalization group transformation, we obtain an effective Hamiltonian for
the full system plus environment that comprises only those environmental
degrees of freedom that are within the effective light cone of the system. The
reduced system dynamics can therefore be simulated with a computational effort
that scales at most polynomially in the interaction time and the size of the
effective light cone. Our results hold for generic environments consisting of
either discrete or continuous degrees of freedom.
