Finding Almost Tight Witness Trees

Authors Dylan Hyatt-Denesik, Afrouz Jabal Ameli, Laura Sanità



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Author Details

Dylan Hyatt-Denesik
  • Eindhoven University of Technology, The Netherlands
Afrouz Jabal Ameli
  • Eindhoven University of Technology, The Netherlands
Laura Sanità
  • Bocconi University, Milano, Italy

Acknowledgements

The authors would like to thank Haris Angelidakis for his valuable discussion on this project. Furthermore, the authors would like to acknowledge the 2021 Hausdorff trimester program "Discrete Optimization", during which this work was started.

Cite AsGet BibTex

Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità. Finding Almost Tight Witness Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.79

Abstract

This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Algorithms
  • Network Design
  • Approximation

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References

  1. David Adjiashvili. Beating approximation factor two for weighted tree augmentation with bounded costs. ACM Trans. Algorithms, 15(2):19:1-19:26, 2019. Google Scholar
  2. Haris Angelidakis, Dylan Hyatt-Denesik, and Laura Sanità. Node connectivity augmentation via iterative randomized rounding. Mathematical Programming, pages 1-37, 2022. Google Scholar
  3. Manu Basavaraju, Fedor V. Fomin, Petr A. Golovach, Pranabendu Misra, M. S. Ramanujan, and Saket Saurabh. Parameterized algorithms to preserve connectivity. In Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP), pages 800-811, 2014. Google Scholar
  4. Jaroslaw Byrka, Fabrizio Grandoni, and Afrouz Jabal Ameli. Breaching the 2-approximation barrier for connectivity augmentation: a reduction to Steiner tree. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 815-825, 2020. Google Scholar
  5. Jaroslaw Byrka, Fabrizio Grandoni, Thomas Rothvoß, and Laura Sanità. Steiner tree approximation via iterative randomized rounding. J. ACM, 60(1):6:1-6:33, 2013. Google Scholar
  6. Federica Cecchetto, Vera Traub, and Rico Zenklusen. Bridging the gap between tree and connectivity augmentation: unified and stronger approaches. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 370-383. ACM, 2021. Google Scholar
  7. Joseph Cheriyan and Zhihan Gao. Approximating (unweighted) tree augmentation via lift-and-project, part I: stemless TAP. Algorithmica, 80(2):530-559, 2018. Google Scholar
  8. Joseph Cheriyan and Zhihan Gao. Approximating (unweighted) tree augmentation via lift-and-project, part II. Algorithmica, 80(2):608-651, 2018. Google Scholar
  9. Efim A Dinitz, Alexander V Karzanov, and Michael V Lomonosov. On the structure of the system of minimum edge cuts in a graph. Issledovaniya po Diskretnoi Optimizatsii, pages 290-306, 1976. Google Scholar
  10. Andreas Emil Feldmann, Jochen Könemann, Neil Olver, and Laura Sanità. On the equivalence of the bidirected and hypergraphic relaxations for steiner tree. Mathematical programming, 160(1):379-406, 2016. Google Scholar
  11. Samuel Fiorini, Martin Groß, Jochen Könemann, and Laura Sanità. Approximating weighted tree augmentation via chvátal-gomory cuts. In Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 817-831. SIAM, 2018. Google Scholar
  12. Greg N. Frederickson and Joseph JáJá. Approximation algorithms for several graph augmentation problems. SIAM J. Comput., 10(2):270-283, 1981. Google Scholar
  13. Michel X. Goemans, Neil Olver, Thomas Rothvoß, and Rico Zenklusen. Matroids and integrality gaps for hypergraphic steiner tree relaxations. In Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, STOC '12, pages 1161-1176, New York, NY, USA, 2012. Association for Computing Machinery. URL: https://doi.org/10.1145/2213977.2214081.
  14. Fabrizio Grandoni, Christos Kalaitzis, and Rico Zenklusen. Improved approximation for tree augmentation: saving by rewiring. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 632-645. ACM, 2018. Google Scholar
  15. Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità. Finding almost tight witness trees, 2023. URL: https://arxiv.org/abs/2211.12431.
  16. Zeev Nutov. 2-node-connectivity network design. In Proceedings of the 18th International Workshop on Approximation and Online Algorithms (WAOA), volume 12806 of Lecture Notes in Computer Science, pages 220-235. Springer, 2020. Google Scholar
  17. Zeev Nutov. Approximation algorithms for connectivity augmentation problems. In Proceedings of the 16th International Computer Science Symposium in Russia (CSR), volume 12730, pages 321-338. Springer, 2021. Google Scholar
  18. Vera Traub and Rico Zenklusen. A (1.5+ε)-approximation algorithm for weighted connectivity augmentation, 2022. URL: https://doi.org/10.48550/arXiv.2209.07860.
  19. Vera Traub and Rico Zenklusen. A better-than-2 approximation for weighted tree augmentation. In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pages 1-12. IEEE, 2022. Google Scholar
  20. Vera Traub and Rico Zenklusen. Local search for weighted tree augmentation and steiner tree. In Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3253-3272. SIAM, 2022. Google Scholar
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