  Motivated by Guo-Luo's generalized circle packings on surfaces with boundary
\cite{GL2}, we introduce the generalized sphere packings on 3-dimensional
manifolds with boundary. Then we investigate the rigidity of the generalized
sphere packing metrics. We prove that the generalized sphere packing metric is
determined by the combinatorial scalar curvature. To find the hyper-ideal
polyhedral metrics on 3-dimensional manifolds with prescribed combinatorial
scalar curvature, we introduce the combinatorial Ricci flow and combinatorial
Calabi flow for the generalized sphere packings on 3-dimensional manifolds with
boundary. Then we study the longtime existence and convergence for the
solutions of these combinatorial curvature flows.
