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We develop an algorithm for reconstructing the triaxial shapes of dark matter halos from the anisotropic spatial distributions of their substructures. First, we construct an analytic model for the anisotropic spatial distributions of dark halo substructures under the assumption that the tidal field with non-zero trace in the triaxial mass distribution of the host halos generate the substructure bulk motions toward the major principal axes of the hosts. Our analytic model reveals 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 fit the analytic model to the numerical results from high-resolution N-body simulation with setting the axis ratios of the triaxial host halo as free parameters, 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

Reconstructing the Triaxial Shapes of Dark Matter Halos from the Anisotropic Spatial Distributions of their Substructures in the Concordance Cosmology