  We propose the redistribution-reconfiguration~(red-rec) algorithm to
efficiently compute control protocols to assemble compact-centered
configurations of atoms in two-dimensional arrays of optical traps with lattice
geometries. The red-rec algorithm redistributes atoms among pairs of
donor-receiver columns and reconfigures each column using an exact
displacement-minimizing algorithm, harnessing parallel control operations that
simultaneously actuate multiple traps to reduce the execution time. We
numerically quantify the performance of the red-rec algorithm, both in the
absence and in the presence of loss, using realistic physical parameters and
operational constraints. We show that the number of traps required to prepare a
compact-centered configuration of atoms on a grid with a mean success
probability of one half scales as the 3/2 power of the number of desired atoms,
highlighting the challenges of assembling configurations of tens of thousands
of atoms. We further demonstrate that faster preparation times can be achieved
by rejecting configurations of atoms containing fewer atoms than a given
threshold. The red-rec algorithm admits an efficient implementation that can
readily be deployed on real-time control systems to assemble large
configurations of atoms with high mean success probability and fast preparation
times.
