Dynamic Maximal Matching in Clique Networks

Authors Minming Li, Peter Robinson, Xianbin Zhu

Thumbnail PDF


  • Filesize: 0.89 MB
  • 21 pages

Document Identifiers

Author Details

Minming Li
  • Department of Computer Science, City University of Hong Kong, Hong Kong
Peter Robinson
  • School of Computer & Cyber Sciences, Augusta University, GA, USA
Xianbin Zhu
  • Department of Computer Science, City University of Hong Kong, Hong Kong

Cite AsGet BibTex

Minming Li, Peter Robinson, and Xianbin Zhu. Dynamic Maximal Matching in Clique Networks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 73:1-73:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of n nodes is vertex-partitioned among k players that communicate via message passing. Our goal is to provide an efficient algorithm that quickly updates the matching even if an adversary determines batches of 𝓁 edge insertions or deletions. We first show a lower bound of Ω((𝓁 log k)/(k²log n)) rounds for recomputing a matching assuming an oblivious adversary who is unaware of the initial (random) vertex partition as well as the current state of the players, and a stronger lower bound of Ω(𝓁/(klog n)) rounds against an adaptive adversary, who may choose any balanced (but not necessarily random) vertex partition initially and who knows the current state of the players. We also present a randomized algorithm that has an initialization time of O(n/(k log n)) rounds, while achieving an update time that that is independent of n: In more detail, the update time is O(⌈𝓁/k⌉ log k) against an oblivious adversary, who must fix all updates in advance. If we consider the stronger adaptive adversary, the update time becomes O (⌈𝓁/√k⌉ log k) rounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • distributed graph algorithm
  • dynamic network
  • maximal matching
  • randomized algorithm
  • lower bound


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


  1. Umut A Acar, Daniel Anderson, Guy E Blelloch, and Laxman Dhulipala. Parallel batch-dynamic graph connectivity. In The 31st ACM Symposium on Parallelism in Algorithms and Architectures, pages 381-392, 2019. Google Scholar
  2. Umut A Acar, Andrew Cotter, Benoît Hudson, and Duru Türkoglu. Parallelism in dynamic well-spaced point sets. In Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures, pages 33-42, 2011. Google Scholar
  3. Daniel Anderson. Parallel Batch-Dynamic Algorithms Dynamic Trees, Graphs, and Self-Adjusting Computation. PhD thesis, Carnegie Mellon University, 2023. Google Scholar
  4. Shiri Antaki, Quanquan C Liu, and Shay Solomon. Near-optimal distributed implementations of dynamic algorithms for symmetry breaking problems. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  5. John Augustine, Kishore Kothapalli, and Gopal Pandurangan. Efficient distributed algorithms in the k-machine model via pram simulations. In 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pages 223-232. IEEE, 2021. Google Scholar
  6. Philipp Bamberger, Fabian Kuhn, and Yannic Maus. Local distributed algorithms in highly dynamic networks. In 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pages 33-42. IEEE, 2019. Google Scholar
  7. Sayan Bandyapadhyay, Tanmay Inamdar, Shreyas Pai, and Sriram V Pemmaraju. Near-optimal clustering in the k-machine model. In Proceedings of the 19th International Conference on Distributed Computing and Networking, pages 1-10, 2018. Google Scholar
  8. Soheil Behnezhad, Mohammad Taghi Hajiaghayi, and David G Harris. Exponentially faster massively parallel maximal matching. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), pages 1637-1649. IEEE, 2019. Google Scholar
  9. Keren Censor-Hillel, Neta Dafni, Victor I Kolobov, Ami Paz, and Gregory Schwartzman. Fast deterministic algorithms for highly-dynamic networks. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2021. Google Scholar
  10. Keren Censor-Hillel, Elad Haramaty, and Zohar Karnin. Optimal dynamic distributed mis. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pages 217-226, 2016. Google Scholar
  11. Keren Censor-Hillel, Victor I Kolobov, and Gregory Schwartzman. Finding subgraphs in highly dynamic networks. In Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures, pages 140-150, 2021. Google Scholar
  12. Avery Ching, Sergey Edunov, Maja Kabiljo, Dionysios Logothetis, and Sambavi Muthukrishnan. One trillion edges: Graph processing at facebook-scale. PVLDB, 8(12):1804-1815, 2015. URL: http://www.vldb.org/pvldb/vol8/p1804-ching.pdf, URL: https://doi.org/10.14778/2824032.2824077.
  13. Laxman Dhulipala, David Durfee, Janardhan Kulkarni, Richard Peng, Saurabh Sawlani, and Xiaorui Sun. Parallel batch-dynamic graphs: Algorithms and lower bounds. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1300-1319. SIAM, 2020. Google Scholar
  14. Klaus-Tycho Foerster, Janne H Korhonen, Ami Paz, Joel Rybicki, and Stefan Schmid. Input-dynamic distributed algorithms for communication networks. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 5(1):1-33, 2021. Google Scholar
  15. Seth Gilbert and Lawrence Er Lu Li. How fast can you update your MST? In Christian Scheideler and Michael Spear, editors, SPAA '20: 32nd ACM Symposium on Parallelism in Algorithms and Architectures, Virtual Event, USA, July 15-17, 2020, pages 531-533. ACM, 2020. URL: https://doi.org/10.1145/3350755.3400240.
  16. Joseph E. Gonzalez, Reynold S. Xin, Ankur Dave, Daniel Crankshaw, Michael J. Franklin, and Ion Stoica. Graphx: Graph processing in a distributed dataflow framework. In USENIX OSDI 2014, pages 599-613, 2014. URL: https://www.usenix.org/conference/osdi14/technical-sessions/presentation/gonzalez.
  17. Khalid Hourani, Hartmut Klauck, William K Moses Jr, Danupon Nanongkai, Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. Distributed algorithms for large-scale graphs. arXiv e-prints, pages arXiv-1311, 2023. Google Scholar
  18. Russell Impagliazzo and Valentine Kabanets. Constructive proofs of concentration bounds. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 13th International Workshop, APPROX 2010, and 14th International Workshop, RANDOM 2010, Barcelona, Spain, September 1-3, 2010. Proceedings, pages 617-631. Springer, 2010. Google Scholar
  19. Amos Israeli and Alon Itai. A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters, 22(2):77-80, 1986. Google Scholar
  20. Giuseppe F Italiano, Silvio Lattanzi, Vahab S Mirrokni, and Nikos Parotsidis. Dynamic algorithms for the massively parallel computation model. In The 31st ACM Symposium on Parallelism in Algorithms and Architectures, pages 49-58, 2019. Google Scholar
  21. Howard Karloff, Siddharth Suri, and Sergei Vassilvitskii. A model of computation for mapreduce. In Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms, pages 938-948. SIAM, 2010. Google Scholar
  22. Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan, and Peter Robinson. Distributed computation of large-scale graph problems. In Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, pages 391-410. SIAM, 2014. Google Scholar
  23. Zvi Lotker, Boaz Patt-Shamir, Elan Pavlov, and David Peleg. Minimum-weight spanning tree construction in O(log log n) communication rounds. SIAM J. Comput., 35(1):120-131, 2005. URL: https://doi.org/10.1137/S0097539704441848.
  24. Grzegorz Malewicz, Matthew H. Austern, Aart J. C. Bik, James C. Dehnert, Ilan Horn, Naty Leiser, and Grzegorz Czajkowski. Pregel: a system for large-scale graph processing. In SIGMOD Conference, pages 135-146, 2010. URL: https://doi.org/10.1145/1807167.1807184.
  25. Krzysztof Nowicki and Krzysztof Onak. Dynamic graph algorithms with batch updates in the massively parallel computation model. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2939-2958. SIAM, 2021. Google Scholar
  26. Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. On the distributed complexity of large-scale graph computations. ACM Transactions on Parallel Computing (TOPC), 8(2):1-28, 2021. Google Scholar
  27. Kenneth H Rosen. Discrete mathematics and its applications. The McGraw Hill Companies, 2007. Google Scholar