A New Approximation Algorithm for the Minimum 2-Edge-Connected Spanning Subgraph Problem

TL;DR

This paper introduces a simplified approximation algorithm for the minimum 2-edge-connected spanning subgraph problem, achieving a 4/3 ratio overall and an improved 6/5 ratio on subcubic graphs, advancing the state of the art.

Contribution

It presents a novel, simpler primal-dual based approximation algorithm with improved ratios for specific graph classes, matching the best known approximation bounds.

Findings

Achieves a 4/3 approximation ratio for the general problem.

Improves the ratio to 6/5 on subcubic graphs.

Simplifies the algorithm and analysis compared to previous methods.

Abstract

We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$ on subcubic graphs, which is an improvement upon the previous best ratio of $\frac{5}{4}$. The algorithm is a novel extension of the primal-dual schema, which consists of two distinct phases. Both the algorithm and the analysis are much simpler than those of the previous approaches.