In the 2-Vertex-Connected Spanning Subgraph problem (2-VCSS), we are given an undirected graph $G$, and the objective is to find a 2-vertex-connected spanning subgraph $S$ of $G$ with the minimum number of edges. In the context of survivable network design, 2-VCSS is one of the most fundamental and well-studied problems. There has been active research on improving the approximation ratio of algorithms, and the current best ratio is $\frac{4}{3}$, achieved by Bosch-Calvo, Grandoni, and Jabal Ameli. In this paper, we improve the approximation ratio to $\frac{95}{72}+\varepsilon$ ($<1.32$). The key idea in our algorithm is to introduce a 2-edge-cover without certain cycle components, and use it as an initial solution.

翻译：在2-顶点连通生成子图问题（2-VCSS）中，给定一个无向图$G$，目标是找到$G$的一个边数最少的2-顶点连通生成子图$S$。在可生存网络设计领域中，2-VCSS是最基本且研究最深入的问题之一。近年来，算法近似比的改进研究一直很活跃，目前最优近似比为$\frac{4}{3}$，由Bosch-Calvo、Grandoni和Jabal Ameli提出。本文将该近似比改进至$\frac{95}{72}+\varepsilon$（$<1.32$）。我们算法的关键思想是引入一个不含特定环分量的2-边覆盖，并将其作为初始解。