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Asynchronous Rumor Spreading in Dynamic Graphs

Authors Bernard Mans , Ali Pourmiri



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Author Details

Bernard Mans
  • Macquarie University, Sydney, Australia
Ali Pourmiri
  • UNSW, Sydney, Australia

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Bernard Mans and Ali Pourmiri. Asynchronous Rumor Spreading in Dynamic Graphs. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 31:1-31:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.OPODIS.2021.31

Abstract

We study asynchronous rumor spreading algorithm in dynamic and static graphs. In the asynchronous rumor spreading, for a given underlying graph, each node is equipped with an exponential time clock of rate 1. When a node’s clock ticks, the node calls a random neighbor in order to exchange a rumor, if at least one of them knows it. Assuming a single node knows a rumor, we apply a differential equation-based technique to obtain an upper bound for the spread time of the algorithm in general dynamic graphs, which is the first time when all nodes get informed with high probability. In particular, we derive an upper bound for the spread time of the algorithm in a discrete version of a geometric mobile network, introduced by Clementi et al. [Andrea E. F. Clementi et al., 2011]. In this model, a set of n agents independently performs random walks on a √n× √n plane and every two agents are able to communicate if they are within Euclidean distance at most R, where f(n)√{log n} ⩽ R ⩽ √n and f(n) is a slowly growing function in n. Here, we show that the algorithm spreads a rumor through the network in 𝒪(log n+√n/R) time, with high probability. Although we only show an upper bound the spread time of the algorithm in a 2 dimensional space, the framework can be also applied for geometric mobile networks defined over higher dimensional space and other random dynamic evolving networks such as stationary edge-Markovian model. Besides these synchronous and discrete dynamic models, we also consider the spreading time in dynamical Erdős-Rényi graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
  • Theory of computation → Network flows
Keywords
  • randomized rumor spreading
  • push/pull
  • asynchronous rumor spreading

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References

  1. Hüseyin Acan, Andrea Collevecchio, Abbas Mehrabian, and Nick Wormald. On the push&pull protocol for rumour spreading: [extended abstract]. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 405-412, 2015. URL: https://doi.org/10.1145/2767386.2767416.
  2. Petra Berenbrink, Robert Elsässer, and Tom Friedetzky. Efficient randomised broadcasting in random regular networks with applications in peer-to-peer systems. In Proc. 27th Symp. Principles of Distributed Computing (PODC), pages 155-164, 2008. Google Scholar
  3. Stephen Boyd, Arpita Ghosh, Balaji Prabhakar, and Devavrat Shah. Randomized gossip algorithms. IEEE Transactions on Information Theory, 52(6):2508-2530, 2006. Google Scholar
  4. Tracy Camp, Jeff Boleng, and Vanessa Davies. A survey of mobility models for ad hoc network research. Wireless Communications and Mobile Computing, 2(5):483-502, 2002. URL: https://doi.org/10.1002/wcm.72.
  5. Flavio Chierichetti, George Giakkoupis, Silvio Lattanzi, and Alessandro Panconesi. Rumor spreading and conductance. J. ACM, 65(4):17:1-17:21, 2018. URL: https://doi.org/10.1145/3173043.
  6. Andrea E. F. Clementi, Pierluigi Crescenzi, Carola Doerr, Pierre Fraigniaud, Marco Isopi, Alessandro Panconesi, Francesco Pasquale, and Riccardo Silvestri. Rumor spreading in random evolving graphs. In Algorithms - ESA 2013 - 21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings, pages 325-336, 2013. URL: https://doi.org/10.1007/978-3-642-40450-4_28.
  7. Andrea E. F. Clementi, Angelo Monti, Francesco Pasquale, and Riccardo Silvestri. Information spreading in stationary markovian evolving graphs. IEEE Trans. Parallel Distrib. Syst., 22(9):1425-1432, 2011. URL: https://doi.org/10.1109/TPDS.2011.33.
  8. Andrea E. F. Clementi, Riccardo Silvestri, and Luca Trevisan. Information spreading in dynamic graphs. In ACM Symposium on Principles of Distributed Computing, PODC '12, Funchal, Madeira, Portugal, July 16-18, 2012, pages 37-46, 2012. URL: https://doi.org/10.1145/2332432.2332439.
  9. D. J. Daley and D. Vere-Jones. An introduction to the theory of point processes. Vol. I. Probability and its Applications (New York). Springer-Verlag, New York, second edition, 2003. Elementary theory and methods. Google Scholar
  10. Alan Demers, Mark Gealy, Dan Greene, Carl Hauser, Wes Irish, John Larson, Sue Manning, Scott Shenker, Howard Sturgis, Dan Swinehart, Doug Terry, and Don Woods. Epidemic algorithms for replicated database maintenance. In Proc. 6th Symp. Principles of Distributed Computing (PODC), pages 1-12, 1987. Google Scholar
  11. Benjamin Doerr, Mahmoud Fouz, and Tobias Friedrich. Social networks spread rumors in sublogarithmic time. In Proc. 43th Symp. Theory of Computing (STOC), pages 21-30, 2011. Google Scholar
  12. Uriel Feige, David Peleg, Prabhakar Raghavan, and Eli Upfal. Randomized broadcast in networks. Random Struct. Algorithms, 1(4):447-460, 1990. Google Scholar
  13. George Giakkoupis, Yasamin Nazari, and Philipp Woelfel. How asynchrony affects rumor spreading time. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC 2016, Chicago, IL, USA, July 25-28, 2016, pages 185-194, 2016. URL: https://doi.org/10.1145/2933057.2933117.
  14. George Giakkoupis, Thomas Sauerwald, and Alexandre Stauffer. Randomized rumor spreading in dynamic graphs. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part II, pages 495-507, 2014. URL: https://doi.org/10.1007/978-3-662-43951-7_42.
  15. Olle Häggström, Yuval Peres, and Jeffrey E. Steif. Dynamical percolation. Ann. Inst. H. Poincaré Probab. Statist., 33(4):497-528, 1997. URL: https://doi.org/10.1016/S0246-0203(97)80103-3.
  16. Mor Harchol-Balter, Frank Thomson Leighton, and Daniel Lewin. Resource discovery in distributed networks. In Proc. 18th Symp. Principles of Distributed Computing (PODC), pages 229-237, 1999. Google Scholar
  17. Dariusz R. Kowalski and Christopher Thraves Caro. Estimating time complexity of rumor spreading in ad-hoc networks. In Jacek Cichon, Maciej Gebala, and Marek Klonowski, editors, Ad-hoc, Mobile, and Wireless Network - 12th International Conference, ADHOC-NOW 2013, Wrocław, Poland, July 8-10, 2013. Proceedings, volume 7960 of Lecture Notes in Computer Science, pages 245-256. Springer, 2013. Google Scholar
  18. Henry Lam, Zhenming Liu, Michael Mitzenmacher, Xiaorui Sun, and Yajun Wang. Information dissemination via random walks in d-dimensional space. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17-19, 2012, pages 1612-1622, 2012. URL: https://doi.org/10.1137/1.9781611973099.128.
  19. László Lovász and Ravi Kannan. Faster mixing via average conductance. In Jeffrey Scott Vitter, Lawrence L. Larmore, and Frank Thomson Leighton, editors, Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, May 1-4, 1999, Atlanta, Georgia, USA, pages 282-287. ACM, 1999. URL: https://doi.org/10.1145/301250.301317.
  20. Konstantinos Panagiotou and Leo Speidel. Asynchronous rumor spreading on random graphs. In Algorithms and Computation - 24th International Symposium, ISAAC 2013, Hong Kong, China, December 16-18, 2013, Proceedings, pages 424-434, 2013. URL: https://doi.org/10.1007/978-3-642-45030-3_40.
  21. Alberto Pettarin, Andrea Pietracaprina, Geppino Pucci, and Eli Upfal. Tight bounds on information dissemination in sparse mobile networks. In Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC 2011, San Jose, CA, USA, June 6-8, 2011, pages 355-362, 2011. URL: https://doi.org/10.1145/1993806.1993882.
  22. Ali Pourmiri and Bernard Mans. Tight analysis of asynchronous rumor spreading in dynamic networks. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2020, Salerno, Italy, 3-7 August 2020, pages 263-272, 2020. Google Scholar
  23. Ali Pourmiri and Fahimeh Ramezani. Ultra-fast asynchronous randomized rumor spreading (brief announcement). In The 31st ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2019, Phoenix, AZ, USA, June 22-24, 2019., pages 81-83, 2019. URL: https://doi.org/10.1145/3323165.3323167.
  24. Perla Sousi and Sam Thomas. Cutoff for random walk on dynamical erdős-rényi graph. arXiv, 2018. URL: http://arxiv.org/abs/1807.04719.
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