  We present a scattering theory for the efficient transmission of an
excitation across a finite network with designed disorder. We show that the
presence of randomly positioned networks sites allows to significantly
accelerate the excitation transfer processes as compared to a dimer structure,
if only the disordered Hamiltonians are constrained to be centrosymmetric, and
to exhibit a dominant doublet in their spectrum. We identify the cause of this
efficiency enhancement in the constructive interplay between disorder-induced
fluctuations of the dominant doublet's splitting and the coupling strength
between the input and output sites to the scattering channels. We find that the
characteristic strength of these fluctuations together with the channel
coupling fully control the transfer efficiency.
