A 5/4-Approximation for Two-Edge Connectivity

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Miguel Bosch-Calvo, Mohit Garg, Fabrizio Grandoni, Felix Hommelsheim, Afrouz Jabal Ameli, Alexander Lindermayr

Published: 2025, Last Modified: 19 Dec 2025STOC 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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 nO(1) instead of nO(1/ε).