A 5/4-Approximation for Two-Edge Connectivity

The 2-Edge-Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected and unweighted graph, the task is to find a spanning subgraph with the minimum number of edges that is 2-edge-connected (i.e., it remains connected after the removal of any single edge). 2ECSS is an NP-hard problem that has been extensively studied in the context of approximation algorithms. The best-known approximation ratio for 2ECSS prior to this work was 1.3+ε, for any constant ε>0 [Garg, Grandoni, Jabal-Ameli’23; Kobayashi, Noguchi’23]. In this paper, we present a 5/4-approximation algorithm. Our algorithm is also faster for small values of ε: its running time is n O (1) instead of n O (1/ε) .

Authors

• Miguel Bosch-Calvo
• Mohit Garg 0003
• Fabrizio Grandoni 0001
• Felix Hommelsheim
• Afrouz Jabal Ameli
• Alexander Lindermayr

Keywords

• 2-edge connectivity
• approximation algorithms
• combinatorial optimization
• network design