5/4-Approximation of Minimum 2-Edge-Connected Spanning Subgraph

We provide a $5/4$-approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. This improves upon the previous best ratio of $4/3$. The algorithm is based on applying local improvement steps on a starting solution provided by a standard ear decomposition together with the idea of running several iterations on residual graphs by excluding certain edges that do not belong to an optimum solution. The latter idea is a novel one, which allows us to bypass $3$-ears with no loss in approximation ratio, the bottleneck for obtaining a performance guarantee below $3/2$. Our algorithm also implies a simpler $7/4$-approximation algorithm for the matching augmentation problem, which was recently treated.