An Approximation Algorithm for 2-Vertex-Connectivity via Cycle-Restricted 2-Edge-Covers
For researchers in survivable network design, this provides a better approximation algorithm for a fundamental problem, though the improvement is incremental.
This paper improves the approximation ratio for the 2-Vertex-Connected Spanning Subgraph problem from 4/3 to 95/72+ε (<1.32) by introducing a cycle-restricted 2-edge-cover as an initial solution.
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.