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The 2-Edge Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected unweighted graph, find a subgraph with the minimum number of edges which is 2-edge-connected (i. e. , it remains connected after the removal of any single edge). This NP-hard problem is well-studied in terms of approximation algorithms. The current-best approximation factor for 2ECSS is 1. 3+ for any constant >0 Garg, Grandoni, Jabal-Ameli'23; Kobayashi, Noguchi'23. In this paper we present a much simpler 9/7 approximation algorithm, and a more complex 5/4 one. Our algorithms are also faster: their running time is n^O (1) instead of n^O (1/).
Bosch-Calvo et al. (2024) studied this question.
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