A 17/12-Approximation Algorithm for 2-Vertex-Connected Spanning Subgraphs on Graphs with Minimum Degree At Least 3

TL;DR

This paper presents a polynomial-time 17/12-approximation algorithm for the minimum-cost 2-vertex-connected spanning subgraph problem in graphs with minimum degree at least 3, using ear-decomposition techniques.

Contribution

It introduces a new approximation algorithm for 2-vertex-connected spanning subgraphs based on ear-decomposition, improving the approximation ratio for graphs with minimum degree at least 3.

Findings

Achieves a 17/12-approximation ratio.

Uses ear-decomposition framework for connectivity problems.

Applicable to graphs with minimum degree ≥ 3.

Abstract

We obtain a polynomial-time 17/12-approximation algorithm for the minimum-cost 2-vertex-connected spanning subgraph problem, restricted to graphs of minimum degree at least 3. Our algorithm uses the framework of ear-decompositions for approximating connectivity problems, which was previously used in algorithms for finding the smallest 2-edge-connected spanning subgraph by Cheriyan, Seb\H{o} and Szigeti (SIAM J.Discrete Math. 2001) who gave a 17/12-approximation algorithm for this problem, and by Seb\H{o} and Vygen (Combinatorica 2014), who improved the approximation ratio to 4/3.