  We develop the Blooming Tree Algorithm, a new technique that uses
spectroscopic redshift data alone to identify the substructures and the
surrounding groups of galaxy clusters, along with their member galaxies. Based
on the estimated binding energy of galaxy pairs, the algorithm builds a binary
tree that hierarchically arranges all the galaxies in the field of view. The
algorithm searches for buds, corresponding to gravitational potential minima on
the binary tree branches; for each bud, the algorithm combines the number of
galaxies, their velocity dispersion and their average pairwise distance into a
parameter that discriminates between the buds that do not correspond to any
substructure or group, and thus eventually die, and the buds that correspond to
substructures and groups, and thus bloom into the identified structures. We
test our new algorithm with a sample of 300 mock redshift surveys of clusters
in different dynamical states; the clusters are extracted from a large
cosmological $N$-body simulation of a $\Lambda$CDM model. We limit our analysis
to substructures and surrounding groups identified in the simulation with mass
larger than $10^{13} h^{-1} M_{\odot}$. With mock redshift surveys with 200
galaxies within 6 $h^{-1}$~Mpc from the cluster center, the technique recovers
$ 80$\% of the real substructures and $ 60$\% of the surrounding groups; in
$57$\% of the identified structures, at least 60\% of the member galaxies of
the substructures and groups belong to the same real structure. These results
improve by roughly a factor of two the performance of the best substructure
identification algorithm currently available, the $\sigma$ plateau algorithm,
and suggest that our Blooming Tree Algorithm can be an invaluable tool for
detecting substructures of galaxy clusters and investigating their complex
dynamics.
