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arXiv · 2603.29582

A Strong Linear Programming Relaxation for Weighted Tree Augmentation

Vincent Cohen-Addad·Marina Drygala·Nathan Klein·Ola Svensson
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Abstract

The Weighted Tree Augmentation Problem (WTAP) is a fundamental network design problem where the goal is to find a minimum-cost set of additional edges (links) to make an input tree 2-edge-connected. While a 2-approximation is standard and the integrality gap of the classic Cut LP relaxation is known to be at least 1.5, achieving approximation factors significantly below 2 has proven challenging. Recent advances of Traub and Zenklusen using local search culminated in a ratio of $1.5+\epsilon$, establishing the state-of-the-art. In this work, we present a randomized approximation algorithm for WTAP with an approximation ratio below 1.49. Our approach is based on designing and rounding a strong linear programming relaxation for WTAP which incorporates variables that represent subsets of edges and the links used to cover them, inspired by lift-and-project methods like Sherali-Adams.

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Vincent Cohen-Addad, Marina Drygala, Nathan Klein, Ola Svensson. 2026-03-31. A Strong Linear Programming Relaxation for Weighted Tree Augmentation. https://arxiv.org/abs/2603.29582

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