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arXiv · 2408.07019

A $5/4$-Approximation for Two-Edge Connectivity

Miguel Bosch-Calvo·Mohit Garg·Fabrizio Grandoni·Felix Hommelsheim·Afrouz Jabal Ameli·Alexander Lindermayr
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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 $1.3+\varepsilon$, for any constant $\varepsilon>0$ [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 $\varepsilon$: its running time is $n^{O(1)}$ instead of $n^{O(1/\varepsilon)}$.

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Miguel Bosch-Calvo, Mohit Garg, Fabrizio Grandoni, Felix Hommelsheim, Afrouz Jabal Ameli, Alexander Lindermayr. 2024-08-13. A $5/4$-Approximation for Two-Edge Connectivity. https://arxiv.org/abs/2408.07019

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