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

TL;DR

This paper introduces a 5/4-approximation algorithm for the NP-hard 2-Edge-Connected Spanning Subgraph problem, improving approximation ratio and computational efficiency over previous methods.

Contribution

It presents the first 5/4-approximation algorithm for 2ECSS with faster runtime for small epsilon values.

Findings

Achieved a 5/4 approximation ratio for 2ECSS.

Faster algorithm for small epsilon values.

Improved upon previous approximation ratios.

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 $n^{O(1/\varepsilon)}$.