The 2-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most
fundamental and well-studied problems in the context of network design. In the
problem, we are given an undirected graph G, and the objective is to find a
2-edge-connected spanning subgraph H of G with the minimum number of
edges. For this problem, a lot of approximation algorithms have been proposed
in the literature. In particular, very recently, Garg, Grandoni, and Ameli gave
an approximation algorithm for 2-ECSS with factor 1.326, which was the best
approximation ratio. In this paper, we give a (1.3+ε)-approximation
algorithm for 2-ECSS, where ε is an arbitrary positive fixed
constant, which improves the previously known best approximation ratio. In our
algorithm, we compute a minimum triangle-free 2-edge-cover in G with the
aid of the algorithm for finding a maximum triangle-free 2-matching given by
Hartvigsen. Then, with the obtained triangle-free 2-edge-cover, we apply the
arguments by Garg, Grandoni, and Ameli