Matching Augmentation via Simultaneous Contractions
Document Open Access Logo

Matching Augmentation via Simultaneous Contractions

Authors Mohit Garg, Felix Hommelsheim, Nicole Megow

PDF
Thumbnail PDF

File

LIPIcs.ICALP.2023.65.pdf
  • Filesize: 0.71 MB
  • 17 pages

Document Identifiers

Author Details

Mohit Garg
  • Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
Felix Hommelsheim
  • Faculty of Mathematics and Computer Science, Universität Bremen, Germany
Nicole Megow
  • Faculty of Mathematics and Computer Science, Universität Bremen, Germany

Funding

  • Garg, Mohit: Supported by SERB Core Research Grant (CRG/2022/001176) on "Optimization under Intractability and Uncertainty”.

Cite As Get BibTex

Mohit Garg, Felix Hommelsheim, and Nicole Megow. Matching Augmentation via Simultaneous Contractions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.65

Abstract

We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a 2-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an approximation ratio of 13/8 = 1.625 improving upon an earlier 5/3-approximation. The improvement builds on a new α-approximation preserving reduction for any α ≥ 3/2 from arbitrary MAP instances to well-structured instances that do not contain certain forbidden structures like parallel edges, small separators, and contractible subgraphs. We further introduce, as key ingredients, the technique of repeated simultaneous contractions and provide improved lower bounds for instances that cannot be contracted.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • matching augmentation
  • approximation algorithms
  • 2-edge-connectivity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

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. Ajit Agrawal, Philip N. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized steiner problem on networks. SIAM J. Comput., 24(3):440-456, 1995. Google Scholar
  3. Étienne Bamas, Marina Drygala, and Ola Svensson. A simple lp-based approximation algorithm for the matching augmentation problem. In IPCO, volume 13265 of Lecture Notes in Computer Science, pages 57-69. Springer, 2022. Google Scholar
  4. Federica Cecchetto, Vera Traub, and Rico Zenklusen. Bridging the gap between tree and connectivity augmentation: unified and stronger approaches. In STOC, pages 370-383. ACM, 2021. Google Scholar
  5. Joe Cheriyan, Jack Dippel, Fabrizio Grandoni, Arindam Khan, and Vishnu V. Narayan. The matching augmentation problem: a 7/4-approximation algorithm. Math. Program., 182(1):315-354, 2020. Google Scholar
  6. Joseph Cheriyan, Robert Cummings, Jack Dippel, and Jasper Zhu. An improved approximation algorithm for the matching augmentation problem. In ISAAC, volume 212 of LIPIcs, pages 38:1-38:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 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. Nachshon Cohen and Zeev Nutov. A (1+ln2)(1+ln2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. Theor. Comput. Sci., 489-490:67-74, 2013. Google Scholar
  10. Jack Edmonds. Paths, trees, and flowers. Canadian Journal of mathematics, 17:449-467, 1965. Google Scholar
  11. Guy Even, Jon Feldman, Guy Kortsarz, and Zeev Nutov. A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2. ACM Trans. Algorithms, 5(2):21:1-21:17, 2009. Google Scholar
  12. Samuel Fiorini, Martin Groß, Jochen Könemann, and Laura Sanità. Approximating weighted tree augmentation via chvátal-gomory cuts. In SODA, pages 817-831. SIAM, 2018. Google Scholar
  13. Mohit Garg, Fabrizio Grandoni, and Afrouz Jabal Ameli. Improved approximation for two-edge-connectivity. In SODA (to appear), 2023. URL: https://arxiv.org/abs/2209.10265.
  14. Mohit Garg, Felix Hommelsheim, and Nicole Megow. Matching augmentation via simultaneous contractions. arXiv preprint, 2022. URL: https://arxiv.org/abs/2211.01912.
  15. Fabrizio Grandoni, Afrouz Jabal Ameli, and Vera Traub. Breaching the 2-approximation barrier for the forest augmentation problem. In STOC, pages 1598-1611. ACM, 2022. Google Scholar
  16. Fabrizio Grandoni, Christos Kalaitzis, and Rico Zenklusen. Improved approximation for tree augmentation: saving by rewiring. In STOC, pages 632-645. ACM, 2018. Google Scholar
  17. Christoph Hunkenschröder, Santosh S. Vempala, and Adrian Vetta. A 4/3-approximation algorithm for the minimum 2-edge connected subgraph problem. ACM Trans. Algorithms, 15(4):55:1-55:28, 2019. Google Scholar
  18. Kamal Jain. A factor 2 approximation algorithm for the generalized steiner network problem. Comb., 21(1):39-60, 2001. Google Scholar
  19. Samir Khuller and Uzi Vishkin. Biconnectivity approximations and graph carvings. J. ACM, 41(2):214-235, 1994. Google Scholar
  20. Guy Kortsarz and Zeev Nutov. A simplified 1.5-approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2. ACM Trans. Algorithms, 12(2):23:1-23:20, 2016. Google Scholar
  21. Guy Kortsarz and Zeev Nutov. Lp-relaxations for tree augmentation. Discret. Appl. Math., 239:94-105, 2018. Google Scholar
  22. Hiroshi Nagamochi. An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree. Discret. Appl. Math., 126(1):83-113, 2003. Google Scholar
  23. Zeev Nutov. On the tree augmentation problem. Algorithmica, 83(2):553-575, 2021. Google Scholar
  24. András Sebő and Jens Vygen. Shorter tours by nicer ears: 7/5-approximation for the graph-tsp, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs. Comb., 34(5):597-629, 2014. Google Scholar
  25. Vera Traub and Rico Zenklusen. A better-than-2 approximation for weighted tree augmentation. In FOCS, pages 1-12. IEEE, 2021. Google Scholar
  26. Vera Traub and Rico Zenklusen. Local search for weighted tree augmentation and steiner tree. In SODA, pages 3253-3272. SIAM, 2022. Google Scholar
  27. David P. Williamson, Michel X. Goemans, Milena Mihail, and Vijay V. Vazirani. A primal-dual approximation algorithm for generalized steiner network problems. Comb., 15(3):435-454, 1995. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact