  We develop a method for optimizing the structure of general binary-tree
multiplexers realized with asymmetric photon routers aiming at improving the
performance of spatially multiplexed single-photon sources. Our procedure
systematically considers all possible binary-tree multiplexers that can be
formed by a certain number of photon routers. Using this method one can select
the multiplexer structure that leads to the highest single-photon probability
for a given set of loss parameters characterizing the system. We determine the
optimal general binary-tree multiplexers for experimentally realizable values
of the transmission coefficients of the photon routers and that of the detector
efficiency. We show that single-photon sources based on such optimal
multiplexers yield higher single-photon probabilities than that can be achieved
with single-photon sources based on any other spatial multiplexer considered in
the literature. Our approach improves the performance of multiplexed
single-photon sources even for small system sizes which is the typical
situation in current experiments.
