  We discuss reduced-scaling strategies employing recently introduced
sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to
describe many-body systems. These strategies utilize properties of the SES-CC
formulations where the equations describing certain classes of sub-systems can
be integrated into a computational flows composed coupled eigenvalue problems
of reduced dimensionality. Additionally, these flows can be determined at the
level of the CC Ansatz by the inclusion of selected classes of cluster
amplitudes, which define the wave function "memory" of possible partitionings
of the many-body system into constituent sub-systems. One of the possible ways
of solving these coupled problems is through implementing procedures, where the
information is passed between the sub-systems in a self-consistent manner. As a
special case, we consider local flow formulations where the so-called local
character of correlation effects can be closely related to properties of
sub-system embedding sub-algebras employing localized molecular basis. We also
generalize flow equations to the time domain and to downfolding methods
utilizing double exponential unitary CC Ansatz (DUCC), where reduced
dimensionality of constituent sub-problems offer a possibility of efficient
utilization of limited quantum resources in modeling realistic systems.
