9/7-Approximation for Two-Edge-Connectivity and Two-Vertex-Connectivity

TL;DR

This paper presents improved approximation algorithms with ratio 9/7 for finding minimum 2-edge-connected and 2-vertex-connected spanning subgraphs, advancing the efficiency of solutions for these connectivity problems.

Contribution

The paper introduces new algorithms achieving a 9/7 approximation ratio for both problems, surpassing previous ratios near 4/3.

Findings

Achieved a 9/7 approximation ratio for 2-edge-connectivity

Achieved a 9/7 approximation ratio for 2-vertex-connectivity

Improved upon previous algorithms with ratios slightly less than 4/3

Abstract

We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio $\frac{9}{7}$. This improves upon a recent algorithm with ratio slightly smaller than $\frac{4}{3}$ for 2-edge-connectivity, and another one with ratio $\frac{4}{3}$ for 2-vertex-connectivity.