# Improved Approximation for Two-Edge-Connectivity

The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the 2-Edge-Connected Spanning Subgraph problem (2-ECSS): given an undirected graph G, find a 2-edge-connected spanning subgraph H of G with the minimum number of edges (in particular, H remains connected after the removal of one arbitrary edge). 2-ECSS is NP-hard and the best-known (polynomial-time) approximation factor for this problem is 4/3. Interestingly, this factor was achieved with drastically different techniques by [Hunkenschröder, Vempala and Vetta '00,'19] and [Sebö and Vygen, '14]. In this paper we present an improved 118/89+ϵ<1.326 approximation for 2-ECSS. The key ingredient in our approach (which might also be helpful in future work) is a reduction to a special type of structured graphs: our reduction preserves approximation factors up to 6/5. While reducing to 2-vertex-connected graphs is trivial (and heavily used in prior work), our structured graphs are "almost" 3-vertex-connected: more precisely, given any 2-vertex-cut {u,v} of a structured graph G=(V,E), G[V∖{u,v}] has exactly 2 connected components, one of which contains exactly one node of degree 2 in G.

• 7 publications
• 22 publications
• 6 publications
research
05/03/2023

### A 4/3 Approximation for 2-Vertex-Connectivity

The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the mo...
research
12/22/2021

### Breaching the 2-Approximation Barrier for the Forest Augmentation Problem

The basic goal of survivable network design is to build cheap networks t...
research
05/30/2022

### Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver

In the k-edge-connected spanning subgraph (kECSS) problem, our goal is t...
research
06/24/2020

### Network connectivity under a probabilistic node failure model

Centrality metrics have been widely applied to identify the nodes in a g...
research
11/03/2022

### Matching Augmentation via Simultaneous Contractions

We consider the matching augmentation problem (MAP), where a matching of...
research
05/29/2020

### Parameterized Complexity of Min-Power Asymmetric Connectivity

We investigate parameterized algorithms for the NP-hard problem Min-Powe...
research
05/26/2019

### Improved Distributed Approximations for Minimum-Weight Two-Edge-Connected Spanning Subgraph

The minimum-weight 2-edge-connected spanning subgraph (2-ECSS) problem i...