In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem. These problems can be viewed as generalizations of the famous Steiner tree packing problem and are closely related to the strong arc decomposition problem. We first prove the NP-completeness for the internally disjoint strong subgraph packing problem restricted to symmetric digraphs and Eulerian digraphs. Then we get inapproximability results for the arc-disjoint strong subgraph packing problem and the internally disjoint strong subgraph packing problem. Finally we study the arc-disjoint strong subgraph packing problem restricted to digraph compositions and obtain some algorithmic results by utilizing the structural properties.

在本文中，我们研究了两种类型的有向强子图封装问题，包括内部不相交强子图封装问题和弧不相交强子图封装问题。这些问题可以看作是著名的施泰纳树打包问题的推广，并且与强弧分解问题密切相关。我们首先证明了仅限于对称有向图和欧拉有向图的内部不相交强子图打包问题的 NP 完全性。然后我们得到了弧不相交强子图打包问题和内部不相交强子图打包问题的不可近似性结果。最后，我们研究了限于有向图组合的弧不相交强子图打包问题，并利用其结构性质获得了一些算法结果。