  We develop an algorithm to reconstruct the triaxial shapes of dark matter
halos from the anisotropic spatial distributions of their substructures for the
concordance background cosmology. First, we construct an analytic model for the
anisotropic spatial distribution of dark halo substructures under the
assumption that the tidal field with non-zero trace in the triaxial mass
distribution of the host halos generates the substructure bulk motions toward
the major principal axes of the hosts. Our analytic model implies that the
degree of anisotropy depends sensitively on the triaxiality of the host halos
as well as the correlation between the substructure locations and the tidal
shear field. Second, we set the axis ratios of the triaxial host halos as free
parameters in the analytic model, fit the model to the numerical results from
high-resolution N-body simulation of the concordance cosmology, and reconstruct
the two axis-ratios of the host halos from the best-fit values of the free
parameters. The comparison of the reconstructed axis ratios with the numerical
results reveals a good agreement. Finally, we conclude that our analytic model
may provide a physical understanding of the anisotropic spatial distribution of
dark halo substructures and a new way to reconstruct in principle the triaxial
shapes of dark matter halos from the observables.
