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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29582 |
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| _version_ | 1866917373297033216 |
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| author | Cohen-Addad, Vincent Drygala, Marina Klein, Nathan Svensson, Ola |
| author_facet | Cohen-Addad, Vincent Drygala, Marina Klein, Nathan Svensson, Ola |
| contents | 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 $1.5+ε$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29582 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Strong Linear Programming Relaxation for Weighted Tree Augmentation Cohen-Addad, Vincent Drygala, Marina Klein, Nathan Svensson, Ola Data Structures and Algorithms 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 $1.5+ε$, 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. |
| title | A Strong Linear Programming Relaxation for Weighted Tree Augmentation |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2603.29582 |