  Sorting atoms stochastically loaded in optical tweezer arrays via an
auxiliary mobile tweezer is an efficient approach to preparing
intermediate-scale defect-free atom arrays in arbitrary geometries. However,
high filling fraction of atom-by-atom assemblers is impeded by redundant
sorting moves with imperfect atom transport, especially for scaling the system
size to larger atom numbers. Here, we propose a new sorting algorithm
(heuristic cluster algorithm, HCA) which provides near-fewest moves in our
tailored atom assembler scheme and experimentally demonstrate a $5\times6$
defect-free atom array with 98.4(7)$\%$ filling fraction for one rearrangement
cycle. The feature of HCA that the number of moves $N_{m}\approx N$ ($N$ is the
number of defect sites to be filled) makes the filling fraction uniform as the
size of atom assembler enlarged. Our method is essential to scale hundreds of
assembled atoms for bottom-up quantum computation, quantum simulation and
precision measurement.
