  We have developed a new geometrical method for identifying and reconstructing
a homogeneous and highly complete set of galaxy groups in the next generation
of deep, flux-limited redshift surveys. Our method combines information from
the three-dimensional Voronoi diagram and its dual, the Delaunay triangulation,
to obtain group and cluster catalogs that are remarkably robust over wide
ranges in redshift and degree of density enhancement. Using the mock DEEP2
catalogs, we demonstrate that the VDM algorithm can be used to identify a
homogeneous set of groups in a magnitude-limited sample ($I\sbr{AB}\le23.5$)
throughout the survey redshift window $0.7 < z < 1.2$. The actual group
membership can be effectively reconstructed even in the distorted redshift
space environment for systems with line of sight velocity dispersion
$\sigma_{los}$ greater than $\approx 200$ \kms. By comparing the galaxy cluster
catalog derived from the mock DEEP2 observations to the underlying distribution
of clusters found in real space with much fainter galaxies included (which
should more closely trace mass in the cluster), we can assess completeness in
velocity dispersion directly. We conclude that the recovered DEEP2 group and
cluster sample should be statistically complete for $\sigma_{los} \gtrsim 400$
\kms. Finally, we argue that the reconstructed bivariate distribution of
systems as a function of redshift and velocity dispersion reproduces with high
fidelity the underlying real space distribution and can thus be used robustly
to constrain cosmological parameters
