  We present a method, PhotoWeb, for estimating photometric redshifts of
individual galaxies, and their equivalent distance, with megaparsec and even
sub-megaparsec accuracy using the Cosmic Web as a constraint over photo-z
estimates. PhotoWeb redshift errors for individual galaxies are of the order of
delta_z = 0.0007, compared to errors of delta_z = 0.02 for current photo-z
techniques. The mean redshift error is of the order of 0.00005-0.0004 compared
to mean errors in the range delta_z =z 0.001-0.01 for the best available
photo-z estimates in the literature. Current photo-z techniques based on the
spectral energy distribution of galaxies and projected clustering produce
redshift estimates with large errors due to the poor constraining power the
galaxy's spectral energy distribution and projected clustering can provide. The
Cosmic Web, on the other hand, provides the strongest constraints on the
position of galaxies. The network of walls, filaments and voids occupy ~%10 of
the volume of the Universe, yet they contain ~%95 of galaxies. The cosmic web,
being a cellular system with well-defined boundaries, sets a restricted set of
intermittent positions a galaxy can occupy along a given line-of-sight. Using
the information in the density field computed from spectroscopic redshifts we
can narrow the possible locations of a given galaxy along the line of sight
from a single broad probability distribution (from photo-z) to one or a few
narrow peaks. Our first results improve previous photo-z errors by more than
one order of magnitude allowing sub-megaparsec errors in some cases. Such
accurate estimates for tens of millions of galaxies will allow unprecedented
galaxy-LSS studies. In this work we apply our technique to the SDSS photo-z
galaxy sample and discuss its performance and future improvements.
