We consider the problem of approximating the smallest 2-vertex connected spanning subgraph (2VCSS) of a 2-vertex connected directed graph, and provide new efficient algorithms. We provide two linear-time algorithms, the first based on a linear-time test for 2-vertex connectivity and divergent spanning trees, and the second based on low-high orders, that correspondingly give 3- and 2-approximations. Then we show that these linear-time algorithms can be combined with an algorithm of Cheriyan and Thurimella that achieves a 3/2-approximation. The combined algorithms preserve the 3/2 approximation guarantee of the Cheriyan-Thurimella algorithm and improve its running time from $O(m^2)$ to $O(m\sqrt{n}+n^2)$, for a digraph with n vertices and m edges. Finally, we present an experimental evaluation of the above algorithms for a variety of input data. The experimental results show that our linear-time algorithms perform very well in practice. Furthermore, the experiments show that the combined algorithms not only improve the running time of the Cheriyan-Thurimella algorithm, but it may also compute a better solution.

我们考虑了逼近2顶点连通有向图的最小2顶点连通跨越子图（2VCSS）的问题，并提供了新的高效算法。我们提供了两种线性时间算法，第一种基于线性时间测试的2顶点连通性和发散的生成树，第二种基于低-高阶，分别给出了3和2近似值。然后，我们证明了这些线性时间算法可以与实现3/2逼近的Cheriyan和Thurimella算法结合使用。组合算法保留了Cheriyan-Thurimella算法的3/2逼近保证，并缩短了算法的运行时间$Ø（{米}^2）$ 至 $Ø（米\sqrt{ñ}+{ñ}^2）$，对于具有n个顶点和m个边的有向图。最后，我们针对各种输入数据提出了上述算法的实验评估。实验结果表明，我们的线性时间算法在实践中表现良好。此外，实验表明，组合算法不仅可以改善Cheriyan-Thurimella算法的运行时间，而且可以计算出更好的解决方案。