A Strong Linear Programming Relaxation for Weighted Tree Augmentation
arXiv:2603.29582v1 Announce Type: new 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 incorp
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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.
Comments: Full version of a paper accepted to STOC 2026
Subjects:
Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2603.29582 [cs.DS]
(or arXiv:2603.29582v1 [cs.DS] for this version)
https://doi.org/10.48550/arXiv.2603.29582
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Marina Drygala [view email] [v1] Tue, 31 Mar 2026 11:03:58 UTC (96 KB)
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