  One of the most significant drawbacks of the all-electron ab initio diffusion
Monte Carlo (DMC) is that its computational cost drastically increases with the
atomic number ($Z$), which typically scales with $Z^{\sim 6}$. In this study,
we introduce an algorithm based on a very efficient implementation of the
Lattice Regularized Diffusion Monte Carlo (LRDMC), where the conventional time
discretization is replaced by its lattice space counterpart. This scheme
enables us to conveniently adopt a small lattice space in the vicinity of
nuclei, and a large one in the valence region, by which a considerable speedup
is achieved, especially for large atomic number $Z$. Indeed, the computational
performances of our algorithm can be theoretically established by using the
Thomas-Fermi model for heavy atoms, yielding an almost affordable scaling with
the atomic number, i.e., $Z^{\sim 5}$. This opens the way for efficient and
accurate all-electron ab initio DMC in electronic structure calculations.
