Before revision:  This gives the first approximation algorithm for dD KS for d > 3. Furthermore, we provide a more sophisticated harmonic-based algorithm, which we call HGaP_k, that is T_{\infty}^{d-1}(1+\epsilon) -asymptotic-approximate for dD BP for the rotational case .
After revision:  This gives the first approximation algorithm for dD KS for d > 3. Furthermore, we provide a more sophisticated harmonic-based algorithm, which we call HGaP_k, having AAR T_{\infty}^{d-1}(1+\epsilon) -asymptotic-approximate for dD BP for the rotational case .