A Better-Than-2 Approximation for Weighted Tree Augmentation

TL;DR

This paper introduces a novel approximation algorithm for the Weighted Tree Augmentation problem that achieves a factor less than 1.7, surpassing the traditional 2-approximation barrier using innovative techniques.

Contribution

The paper presents the first algorithm for Weighted Tree Augmentation with an approximation ratio below 2, specifically under 1.7, breaking a long-standing barrier.

Findings

Achieves approximation factor < 1.7 for Weighted Tree Augmentation

First to surpass the 2-approximation barrier for this problem

Uses new techniques beyond standard methods

Abstract

We present an approximation algorithm for Weighted Tree Augmentation with approximation factor $1+\ln 2 + \varepsilon < 1.7$. This is the first algorithm beating the longstanding factor of $2$, which can be achieved through many standard techniques.