  We implement an efficient strong-disorder renormalization-group (SDRG)
procedure to study disordered tight-binding models in any dimension and on the
Erdos-Renyi random graphs, which represent an appropriate infinite dimensional
limit. Our SDRG algorithm is based on a judicious elimination of most
(irrelevant) new bonds generated under RG. It yields excellent agreement with
exact numerical results for universal properties at the critical point without
significant increase of computer time, and confirm that, for Anderson
localization, the upper critical dimension duc = infinite. We find excellent
convergence of the relevant 1/d expansion down to d=2, in contrast to the
conventional 2+epsilon expansion, which has little to say about what happens in
any d>3. We show that the mysterious mirror symmetry of the conductance scaling
function is a genuine strong-coupling effect, as speculated in early work. This
opens an efficient avenue to explore the critical properties of Anderson
transition in the strong-coupling limit in high dimensions.
