  We study the evolution of the halo-halo correlation function and bias in a
LCDM model using very high-resolution N-body simulations. The high force and
mass resolution allows dark matter (DM) halos to survive in the tidal fields in
high-density regions and thus prevents the ambiguities related with the
``overmerging problem.'' Numbers of galaxy-size halos in cluster-like objects
in our simulation are similar to the numbers of galaxies observed in real
clusters. This allows us to estimate for the first time the evolution of the
correlation function and bias at small (down to ~100/h kpc) scales. We compare
particle distribution, dark matter correlation function, density profiles, and
halo mass function produced with our N-body code and corresponding results of
the AP3M simulations.
  We find that at all epochs the 2-point correlation function of galaxy-size
halos xihh is well approximated by a power-law with slope ~1.6-1.8. The
difference between the shape of xihh and the shape of the correlation function
of matter results in the scale-dependent bias at scales <7/h Mpc, which we find
to be a generic prediction of the hierarchical models, independent of the epoch
and of the model details. We find that our results agree well with existing
clustering data at different redshifts, indicating the general success of the
picture of structure formation in which galaxies form inside the host DM halos.
Particularly, we find an excellent agreement in both slope and the amplitude
between xihh(z=0) in our simulation and the galaxy correlation function
measured using the APM galaxy survey. At high redshifts, the observed
clustering of the Lyman-break galaxies is also reasonably well reproduced by
the models.
