An Approximation Algorithm for 2-Vertex-Connectivity via Cycle-Restricted 2-Edge-Covers

TL;DR

This paper presents an improved approximation algorithm for the 2-Vertex-Connected Spanning Subgraph problem, reducing the ratio to below 1.32 by using cycle-restricted 2-edge-covers as initial solutions.

Contribution

It introduces a novel approach using cycle-restricted 2-edge-covers to achieve a better approximation ratio for 2-VCSS.

Findings

Achieved an approximation ratio of less than 1.32.

Introduced a cycle-restricted 2-edge-cover technique.

Improved upon the previous best ratio of 4/3.

Abstract

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.