Breaching the 2-approximation barrier for the forest augmentation problem

  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},
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… 

Figures from this paper

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

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

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

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

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

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

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.

Breaching the 2-approximation barrier for connectivity augmentation: a reduction to Steiner tree

This paper breaches the 2 approximation barrier for CacAP, hence for CAP, by presenting a polynomial-time 2ln(4)−967/1120+є<1.91 approximation and using a reduction to the Steiner tree problem which was previously used in parameterized algorithms.

Bridging the gap between tree and connectivity augmentation: unified and stronger approaches

This work first bridges the gap between TAP and CAP, by presenting techniques that allow for leveraging insights and methods from TAP to approach CAP, and introduces a new way to get approximation factors below 1.5, based on a new analysis technique.

On the Cycle Augmentation Problem: Hardness and Approximation Algorithms

This paper presents a combinatorial 32+ε-approximation for CycAP, and shows that it is APX-hard, and considers the special case where the input cactus consists of a single cycle, the Cycle Augmentation Problem (CycAP).

Beating Approximation Factor Two for Weighted Tree Augmentation with Bounded Costs

This work presents the first improved approximation algorithm for WTAP in more than three decades and improves this factor to 5/3+ε, which is the ratio between the largest and the smallest cost of any link.

Improved approximation for tree augmentation: saving by rewiring

A new approximation algorithm for O(1)-wide tree instances with approximation guarantee strictly below 1.458 is presented, based on one of their fundamental properties: wide trees naturally decompose into smaller subtrees with a constant number of leaves.

Hardness of Approximation for Vertex-Connectivity Network-Design Problems

The first lower bound on the approximability of SNDP is given, showing that the problem admits no efficient 2log1-?n ratio approximation for any fixed ?

Approximating Weighted Tree Augmentation via Chvátal-Gomory Cuts

This paper improves Adjiashvili's approximation to a [EQUATION]-approximation for WTAP under the bounded cost assumption, and introduces a strong LP that combines [EquATION]-Chvatal-Gomory cuts for the standard LP for the problem with bundle constraints from AdjiASHvili.

A (1 + ln 2)-Approximation Algorithm for Minimum-Cost 2-Edge-Connectivity Augmentation of Trees with Constant Radius

A (1 + ln 2)-approximation algorithm for trees of constant radius is given, based on a new decomposition of problem solutions, which may be of independent interest.

A Simplified 1.5-Approximation Algorithm for Augmenting Edge-Connectivity of a Graph from 1 to 2

This work gives a correct, different, and self-contained proof of the ratio 1.5 that is also substantially simpler and shorter than the previous proofs.