Improved Approximation for Tree Augmentation: Saving by Rewiring

TL;DR

This paper introduces a new approximation algorithm for the Tree Augmentation Problem that improves the previous best ratio of 1.5 to 1.458, using novel techniques.

Contribution

It presents the first approximation algorithm for TAP with a ratio below 1.5, advancing the state of the art.

Findings

Achieved a 1.458-approximation ratio for TAP.

Developed new techniques for better approximation guarantees.

Improved upon the previous best ratio of 1.5.

Abstract

The Tree Augmentation Problem (TAP) is a fundamental network design problem in which we are given a tree and a set of additional edges, also called \emph{links}. The task is to find a set of links, of minimum size, whose addition to the tree leads to a $2$-edge-connected graph. A long line of results on TAP culminated in the previously best known approximation guarantee of $1.5$ achieved by a combinatorial approach due to Kortsarz and Nutov [ACM Transactions on Algorithms 2016], and also by an SDP-based approach by Cheriyan and Gao [Algorithmica 2017]. Moreover, an elegant LP-based $(1.5+\epsilon)$-approximation has also been found very recently by Fiorini, Gro\ss, K\"onemann, and Sanit\'a [SODA 2018]. In this paper, we show that an approximation factor below $1.5$ can be achieved, by presenting a $1.458$-approximation that is based on several new techniques.