Document Open Access Logo

A 0.51-Approximation of Maximum Matching in Sublinear n^{1.5} Time

Authors Sepideh Mahabadi , Mohammad Roghani , Jakub Tarnawski

PDF HTML 5

Files

Thumbnail PDF
PDF
LIPIcs.ICALP.2025.116.pdf
  • Filesize: 0.96 MB
  • 17 pages
HTML5 Logo HTML (experimental)
LIPIcs.ICALP.2025.116.html

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Sublinear Algorithms
  • Maximum Matching
  • Maximal Matching
  • Approximation Algorithm

Metrics

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

Abstract

We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a 0.5109-approximation algorithm with a running time of Õ(n√n).
All previous algorithms either provide only a marginal improvement (e.g., 2^{-280}) over the 0.5-approximation that arises from estimating a maximal matching, or have a running time that is nearly n². Our approach is also arguably much simpler than other algorithms beating 0.5-approximation.

Cite As Get BibTex

Sepideh Mahabadi, Mohammad Roghani, and Jakub Tarnawski. A 0.51-Approximation of Maximum Matching in Sublinear n^{1.5} Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 116:1-116:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.116

Author Details

Sepideh Mahabadi
  • Microsoft Research, Redmond, WA, USA
Mohammad Roghani
  • Stanford University, CA, USA
Jakub Tarnawski
  • Microsoft Research, Redmond, WA, USA

Acknowledgements

This work was done while Mohammad Roghani was an intern at Microsoft Research. The work was conducted in part while Sepideh Mahabadi was long-term visitor at the Simons Institute for the Theory of Computing as part of the Sublinear Algorithms program.

References

  1. Noga Alon, Ronitt Rubinfeld, Shai Vardi, and Ning Xie. Space-Efficient Local Computation Algorithms. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17-19, 2012, pages 1132-1139, 2012. URL: https://doi.org/10.1137/1.9781611973099.89.
  2. Amir Azarmehr, Soheil Behnezhad, and Mohammad Roghani. Fully dynamic matching: (2-√2)-approximation in polylog update time. In David P. Woodruff, editor, Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024, pages 3040-3061. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.109.
  3. Soheil Behnezhad. Time-optimal sublinear algorithms for matching and vertex cover. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 873-884. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00089.
  4. Soheil Behnezhad. Dynamic algorithms for maximum matching size. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 129-162. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.CH6.
  5. Soheil Behnezhad, Mohammad Roghani, and Aviad Rubinstein. Local computation algorithms for maximum matching: New lower bounds. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 2322-2335. IEEE, 2023. URL: https://doi.org/10.1109/FOCS57990.2023.00143.
  6. Soheil Behnezhad, Mohammad Roghani, and Aviad Rubinstein. Sublinear time algorithms and complexity of approximate maximum matching. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 267-280, 2023. URL: https://doi.org/10.1145/3564246.3585231.
  7. Soheil Behnezhad, Mohammad Roghani, and Aviad Rubinstein. Approximating maximum matching requires almost quadratic time. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, pages 444-454, 2024. URL: https://doi.org/10.1145/3618260.3649785.
  8. Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Beating greedy matching in sublinear time. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 3900-3945. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.CH151.
  9. Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Sublinear algorithms for TSP via path covers. CoRR, abs/2301.05350, 2023. URL: https://doi.org/10.48550/arXiv.2301.05350.
  10. Sayan Bhattacharya, Peter Kiss, and Thatchaphol Saranurak. Dynamic (1+ε)-approximate matching size in truly sublinear update time. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 1563-1588. IEEE, 2023. Google Scholar
  11. Sayan Bhattacharya, Peter Kiss, and Thatchaphol Saranurak. Sublinear algorithms for (1.5+ε)-approximate matching. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 254-266, 2023. URL: https://doi.org/10.1145/3564246.3585252.
  12. Sayan Bhattacharya, Peter Kiss, Thatchaphol Saranurak, and David Wajc. Dynamic matching with better-than-2 approximation in polylogarithmic update time. In Nikhil Bansal and Viswanath Nagarajan, editors, Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, January 22-25, 2023, pages 100-128. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977554.CH5.
  13. Yu Chen, Sampath Kannan, and Sanjeev Khanna. Sublinear algorithms and lower bounds for metric tsp cost estimation. arXiv preprint arXiv:2006.05490, 2020. URL: https://arxiv.org/abs/2006.05490.
  14. Mohsen Ghaffari. Local computation of maximal independent set. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, Denver, CO, USA, October 31 - November 3, 2022, pages 438-449, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00049.
  15. Michael Kapralov, Slobodan Mitrović, Ashkan Norouzi-Fard, and Jakab Tardos. Space efficient approximation to maximum matching size from uniform edge samples. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1753-1772. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.107.
  16. Christian Konrad and Kheeran K. Naidu. On two-pass streaming algorithms for maximum bipartite matching. In Mary Wootters and Laura Sanità, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021, August 16-18, 2021, University of Washington, Seattle, Washington, USA (Virtual Conference), volume 207 of LIPIcs, pages 19:1-19:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.APPROX/RANDOM.2021.19.
  17. Reut Levi, Ronitt Rubinfeld, and Anak Yodpinyanee. Local computation algorithms for graphs of non-constant degrees. Algorithmica, 77(4):971-994, 2017. URL: https://doi.org/10.1007/S00453-016-0126-Y.
  18. Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski, and Ali Vakilian. Sublinear Metric Steiner Tree via Improved Bounds for Set Cover. In Raghu Meka, editor, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025), volume 325 of Leibniz International Proceedings in Informatics (LIPIcs), pages 74:1-74:24, Dagstuhl, Germany, 2025. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ITCS.2025.74.
  19. Huy N Nguyen and Krzysztof Onak. Constant-time approximation algorithms via local improvements. In 2008 49th annual IEEE symposium on foundations of computer science, pages 327-336. IEEE, 2008. URL: https://doi.org/10.1109/FOCS.2008.81.
  20. Michal Parnas and Dana Ron. Approximating the Minimum Vertex Cover in Sublinear Time and a Connection to Distributed Algorithms. Theor. Comput. Sci., 381(1-3):183-196, 2007. URL: https://doi.org/10.1016/J.TCS.2007.04.040.
  21. Ronitt Rubinfeld, Gil Tamir, Shai Vardi, and Ning Xie. Fast local computation algorithms. In Innovations in Computer Science - ICS 2011, Tsinghua University, Beijing, China, January 7-9, 2011. Proceedings, pages 223-238, 2011. URL: http://conference.iiis.tsinghua.edu.cn/ICS2011/content/papers/36.html.
  22. Yuichi Yoshida, Masaki Yamamoto, and Hiro Ito. An improved constant-time approximation algorithm for maximum matchings. In Michael Mitzenmacher, editor, Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, May 31 - June 2, 2009, pages 225-234. ACM, 2009. URL: https://doi.org/10.1145/1536414.1536447.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact