# Breaching the 2-approximation barrier for the forest augmentation problem

@article{Grandoni2021BreachingT2, title={Breaching the 2-approximation barrier for the forest augmentation problem}, author={Fabrizio Grandoni and Afrouz Jabal Ameli and Vera Traub}, journal={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing}, year={2021} }

The basic goal of survivable network design is to build cheap networks that guarantee the connectivity of certain pairs of nodes despite the failure of a few edges or nodes. A celebrated result by Jain [Combinatorica'01] provides a 2-approximation for a wide class of these problems. However nothing better is known even for very basic special cases, raising the natural question whether any improved approximation factor is possible at all. In this paper we address one of the most basic problems…

## 6 Citations

### A $(1.5+\epsilon)$-Approximation Algorithm for Weighted Connectivity Augmentation

- Computer Science
- 2022

A well-chosen local search algorithm is designed for WCAP, and it is proved that an optimum solution can be decomposed into smaller components, at least one of which leads to a good local search step as long as the claimed approximation guarantee is achieved.

### Improved Approximation for Two-Edge-Connectivity

- Mathematics, Computer ScienceSODA
- 2023

An improved $\frac{118}{89}+\epsilon<1.326$ approximation for 2-ECSS is presented: the key ingredient in this approach is a reduction to a special type of structured graphs: the reduction preserves approximation factors up to $6/5$.

### A Simple LP-Based Approximation Algorithm for the Matching Augmentation Problem

- Computer ScienceIPCO
- 2022

A simple algorithm is proposed that, guided by an optimal solution to the cut LP, first selects a DFS tree and then finds a solution to MAP by computing an optimum augmentation of this tree and it is shown that this algorithm always returns a better than 2-approximation when compared to thecut LP.

### Steiner Connectivity Augmentation and Splitting-off in Poly-logarithmic Maximum Flows

- Computer Science, MathematicsSODA
- 2023

We give an almost-linear time algorithm for the Steiner connectivity augmentation problem: given an undirected graph, find a smallest (or minimum weight) set of edges whose addition makes a given set…

### An Approximation Algorithm for Two-Edge-Connected Subgraph Problem via Triangle-free Two-Edge-Cover

- Mathematics, Computer Science
- 2023

This paper gives a $(1.3+\varepsilon)-approximation algorithm for 2-ECSS, where $\varpsilon$ is an arbitrary positive fixed constant, which improves the previously known best approximation ratio.

### Matching Augmentation via Simultaneous Contractions

- Mathematics, Computer ScienceArXiv
- 2022

A polynomial-time algorithm with an approximation ratio of $13/8 = 1.625$ improving upon an earlier $5/3$-approximation, and introducing the technique of repeated simultaneous contractions to provide improved lower bounds for instances that cannot be contracted.

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