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Decremental Matching in General Weighted Graphs

Author Aditi Dudeja

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LIPIcs.ICALP.2024.59.pdf
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Author Details

Aditi Dudeja
  • University of Salzburg, Austria

Funding

  • Dudeja, Aditi: This work is supported by Austrian Science Fund (FWF): P 32863-N. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 947702).

Acknowledgements

Thanks to Aaron Bernstein, Sebastian Forster, Yasamin Nazari, and anonymous ICALP reviewers for valuable feedback.

Cite As Get BibTex

Aditi Dudeja. Decremental Matching in General Weighted Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.59

Abstract

In this paper, we consider the problem of maintaining a (1-ε)-approximate maximum weight matching in a dynamic graph G, while the adversary makes changes to the edges of the graph. In the fully dynamic setting, where both edge insertions and deletions are allowed, Gupta and Peng [Manoj Gupta and Richard Peng, 2013] gave an algorithm for this problem with an update time of Õ_ε(√m). We study a natural relaxation of this problem, namely the decremental model, where the adversary is only allowed to delete edges. For the unweighted version of this problem in general (possibly, non-bipartite) graphs, [Sepehr Assadi et al., 2022] gave a decremental algorithm with update time O_ε(poly(log n)). However, beating Õ_ε(√m) update time remained an open problem for the weighted version in general graphs. In this paper, we bridge the gap between unweighted and weighted general graphs for the decremental setting. We give a O_ε(poly(log n)) update time algorithm that maintains a (1-ε) approximate maximum weight matching under adversarial deletions. Like the decremental algorithm of [Sepehr Assadi et al., 2022], our algorithm is randomized, but works against an adaptive adversary. It also matches the time bound for the unweighted version upto dependencies on ε and a log R factor, where R is the ratio between the maximum and minimum edge weight in G.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Weighted Matching
  • Dynamic Algorithms
  • Adaptive Adversary

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References

  1. Kook Jin Ahn and Sudipto Guha. Linear programming in the semi-streaming model with application to the maximum matching problem. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Zurich, Switzerland, July 4-8, 2011, Proceedings, Part II, pages 526-538, 2011. Google Scholar
  2. Sepehr Assadi, Soheil Behnezhad, Sanjeev Khanna, and Huan Li. On regularity lemma and barriers in streaming and dynamic matching. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, FL, USA, June 20-23, 2023, pages 131-144. ACM, 2023. URL: https://doi.org/10.1145/3564246.3585110.
  3. Sepehr Assadi, Aaron Bernstein, and Aditi Dudeja. Decremental matching in general graphs. In 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4-8, 2022, Paris, France, volume 229 of LIPIcs, pages 11:1-11:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.11.
  4. Sepehr Assadi, Sanjeev Khanna, and Yang Li. The stochastic matching problem with (very) few queries. ACM Transactions on Economics and Computation (TEAC), 7(3):1-19, 2019. Google Scholar
  5. Amir Azarmehr, Soheil Behnezhad, and Mohammad Roghani. Fully dynamic matching: (2-√2)-approximation in polylog update time. CoRR, abs/2307.08772, 2023. URL: https://doi.org/10.48550/arXiv.2307.08772.
  6. Soheil Behnezhad. Dynamic algorithms for maximum matching size. In 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.
  7. Soheil Behnezhad and Sanjeev Khanna. New trade-offs for fully dynamic matching via hierarchical EDCS. In Proceedings of the 2022 ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, Virtual Conference / Alexandria, VA, USA, January 9 - 12, 2022, pages 3529-3566. SIAM, 2022. URL: https://doi.org/10.1137/1.9781611977073.140.
  8. Aaron Bernstein, Aditi Dudeja, and Zachary Langley. A framework for dynamic matching in weighted graphs. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 668-681. ACM, 2021. URL: https://doi.org/10.1145/3406325.3451113.
  9. Aaron Bernstein, Maximilian Probst Gutenberg, and Thatchaphol Saranurak. Deterministic decremental reachability, scc, and shortest paths via directed expanders and congestion balancing. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 1123-1134. IEEE, 2020. Google Scholar
  10. Sayan Bhattacharya and Peter Kiss. Deterministic rounding of dynamic fractional matchings. In 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), volume 198 of LIPIcs, pages 27:1-27:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.ICALP.2021.27.
  11. Sayan Bhattacharya, Peter Kiss, and Thatchaphol Saranurak. Dynamic dollar(1+ε)dollar-approximate matching size in truly sublinear update time. CoRR, abs/2302.05030, 2023. URL: https://doi.org/10.48550/arXiv.2302.05030.
  12. Sayan Bhattacharya, Peter Kiss, Thatchaphol Saranurak, and David Wajc. Dynamic matching with better-than-2 approximation in polylogarithmic update time. In 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. Sayan Bhattacharya, Peter Kiss, Aaron Sidford, and David Wajc. Near-optimal dynamic rounding of fractional matchings in bipartite graphs. CoRR, abs/2306.11828, 2023. URL: https://doi.org/10.48550/arXiv.2306.11828.
  14. Joakim Blikstad and Peter Kiss. Incremental (1-ε)-approximate dynamic matching in o(poly(1/ε)) update time. In 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands, volume 274 of LIPIcs, pages 22:1-22:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.ESA.2023.22.
  15. Jiale Chen, Aaron Sidford, and Ta-Wei Tu. Entropy regularization and faster decremental matching in general graphs. arXiv preprint arXiv:2312.09077, 2023. Google Scholar
  16. Ran Duan and Seth Pettie. Linear-time approximation for maximum weight matching. Journal of the ACM (JACM), 61(1):1-23, 2014. Google Scholar
  17. Devdatt P. Dubhashi and Alessandro Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press, 2009. URL: http://www.cambridge.org/gb/knowledge/isbn/item2327542/.
  18. Fabrizio Grandoni, Stefano Leonardi, Piotr Sankowski, Chris Schwiegelshohn, and Shay Solomon. (1 + ε)-approximate incremental matching in constant deterministic amortized time. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pages 1886-1898. SIAM, 2019. URL: https://doi.org/10.1137/1.9781611975482.114.
  19. Manoj Gupta. Maintaining approximate maximum matching in an incremental bipartite graph in polylogarithmic update time. In FSTTCS, 2014. Google Scholar
  20. Manoj Gupta and Richard Peng. Fully dynamic (1+ e)-approximate matchings. 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pages 548-557, 2013. Google Scholar
  21. Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai, and Thatchaphol Saranurak. Unifying and strengthening hardness for dynamic problems via the online matrix-vector multiplication conjecture. In Proceedings of the forty-seventh annual ACM symposium on Theory of computing, pages 21-30, 2015. Google Scholar
  22. Arun Jambulapati, Yujia Jin, Aaron Sidford, and Kevin Tian. Regularized box-simplex games and dynamic decremental bipartite matching. In 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4-8, 2022, Paris, France, volume 229 of LIPIcs, pages 77:1-77:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.ICALP.2022.77.
  23. Tsvi Kopelowitz, Seth Pettie, and Ely Porat. Higher lower bounds from the 3sum conjecture. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 1272-1287. SIAM, 2016. Google Scholar
  24. Daniel Dominic Sleator and Robert Endre Tarjan. A data structure for dynamic trees. J. Comput. Syst. Sci., 26(3):362-391, 1983. URL: https://doi.org/10.1016/0022-0000(83)90006-5.
  25. Daniel Stubbs and Virginia Vassilevska Williams. Metatheorems for dynamic weighted matching. In 8th Innovations in Theoretical Computer Science Conference, ITCS 2017, January 9-11, 2017, Berkeley, CA, USA, volume 67 of LIPIcs, pages 58:1-58:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPICS.ITCS.2017.58.
  26. David Wajc. Rounding dynamic matchings against an adaptive adversary. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pages 194-207, 2020. Google Scholar
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