Abstract
Flooding is a fundamental concept in distributed computing. In flooding, typically, a node forwards a message to its neighbors for the first time when it receives a message. Later if the node receives the same message again, it simply ignores the message and does not forward it. The nodes store a “message record” to ensure that the same message is not forwarded again.
Hussak and Trehan [STACS’20] introduced amnesiac flooding where nodes do not require to keep the message record. They established a surprising result that the amnesic flooding of a single (\(k=1\)) message starting from some source node always terminates in bipartite graphs in e rounds and in non-bipartite graphs in \(e<j\le e+D+1\) rounds, where e is the eccentricity of the source node and D is the diameter of the graph. Recently, Hussak and Trehan [arXiv’20] introduced dynamic amnesiac flooding initiated in possibly multiple rounds with possibly multiple (\(k>1\)) messages from possibly multiple source nodes. They showed that the partial-send case where a node only sends a message to neighbours from which it did not receive any message in the previous round and the ranked full-send case where a node sends some highest ranked message to all neighbors from which it did not receive that message in the previous round, both terminate. However, they showed that the unranked full-send case, where a node sends some random message (not necessarily the highest ranked message) to all the neighbors from which it did not receive that message in the previous round, does not terminate.
In this paper, we show that the unranked full-send case also terminates, provided that diameter D is known to graph nodes. We further show that the termination time is \(D\cdot (2k-1)\) rounds in bipartite graphs and \((2D+1)\cdot (2k-1)\) rounds in non-bipartite graphs.
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Notes
- 1.
In the asynchronous message passing framework, it was shown by Hussak and Trehan [11] that amnesiac flooding does not terminate.
- 2.
If eccentricity \(e_1,e_2,\ldots ,e_{k'}\) of the \(k'\) source nodes is known instead of D, then the bounds translate to \(e_{\max } \cdot (2k-1)\) in bipartite graphs and \((2e_{\max }+1)\cdot (2k-1)\) in non-bipartite graphs with memory \(O(\log (\max \{k,e_{\max }\}))\) bits, where \(e_{\max }:=\max _{1\le l\le k'} e_l.\)
References
Ahmadi, M., Kuhn, F., Kutten, S., Molla, A.R., Pandurangan, G.: The communication cost of information spreading in dynamic networks. In: Proceedings of 39th IEEE International Conference on Distributed Computing Systems (ICDCS), pp. 368–378 (2019)
Attiya, H., Welch, J.L.: Distributed Computing - Fundamentals, Simulations, and Advanced Topics. Wiley Series on Parallel and Distributed Computing, 2nd edn. Wiley, Hoboken (2004)
Borokhovich, M., Avin, C., Lotker, Z.: Tight bounds for algebraic gossip on graphs. In: IEEE International Symposium on Information Theory, ISIT 2010, Austin, Texas, USA, 13–18 June 2010, Proceedings, pp. 1758–1762 (2010)
Boyd, S.P., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)
Chen, J., Pandurangan, G.: Almost-optimal gossip-based aggregate computation. SIAM J. Comput. 41(3), 455–483 (2012)
Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC ’11, pp. 21–30. Association for Computing Machinery, New York (2011). https://doi.org/10.1145/1993636.1993640
Dutta, C., Pandurangan, G., Rajaraman, R., Sun, Z., Viola, E.: On the complexity of information spreading in dynamic networks. In: SODA, pp. 717–736 (2013)
Elsässer, R., Sauerwald, T.: The power of memory in randomized broadcasting. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 218–227 (2008)
Ghaffari, M., Li, J.: Improved distributed algorithms for exact shortest paths. In: STOC, pp. 431–444 (2018)
Holzer, S., Wattenhofer, R.: Optimal distributed all pairs shortest paths and applications. In: PODC, pp. 355–364 (2012)
Hussak, W., Trehan, A.: On the termination of flooding. In: STACS, pp. 17:1–17:13 (2020)
Hussak, W., Trehan, A.: Terminating cases of flooding. CoRR abs/2009.05776 (2020). https://arxiv.org/abs/2009.05776
Kshemkalyani, A.D., Singhal, M.: Distributed Computing: Principles, Algorithms, and Systems. Cambridge University Press, Cambridge (2011)
Kutten, S., Pandurangan, G., Peleg, D., Robinson, P., Trehan, A.: On the complexity of universal leader election. J. ACM 62(1), 7:1–7:27 (2015). https://doi.org/10.1145/2699440
Kutten, S., Pandurangan, G., Peleg, D., Robinson, P., Trehan, A.: Sublinear bounds for randomized leader election. Theor. Comput. Sci. 561, 134–143 (2015). https://doi.org/10.1016/j.tcs.2014.02.009
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco (1996)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, USA (2000)
Rahman, A., Olesinski, W., Gburzynski, P.: Controlled flooding in wireless ad-hoc networks. In: International Workshop on Wireless Ad-Hoc Networks, pp. 73–78 (2004)
Sarma, A.D., Molla, A.R., Pandurangan, G.: Distributed computation in dynamic networks via random walks. Theor. Comput. Sci. 581, 45–66 (2015)
Tanenbaum, A.S., Wetherall, D.J.: Computer Networks, 5th edn. Prentice Hall Press, Hoboken (2010)
Tel, G.: Introduction to Distributed Algorithms, 2nd edn. Cambridge University Press, Cambridge (2001)
Topkis, D.M.: Concurrent broadcast for information dissemination. IEEE Trans. Softw. Eng. 11(10), 1107–1112 (1985)
Turau, V.: Analysis of amnesiac flooding. CoRR abs/2002.10752 (2020). https://arxiv.org/abs/2002.10752
Turau, V.: Stateless information dissemination algorithms. In: Richa, A.W., Scheideler, C. (eds.) SIROCCO 2020. LNCS, vol. 12156, pp. 183–199. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-54921-3_11
Turau, V., et al.: Amnesiac flooding: synchronous stateless information dissemination. In: Bureš, T. (ed.) SOFSEM 2021. LNCS, vol. 12607, pp. 59–73. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-67731-2_5
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Bayramzadeh, Z., Kshemkalyani, A.D., Molla, A.R., Sharma, G. (2021). Weak Amnesiac Flooding of Multiple Messages. In: Echihabi, K., Meyer, R. (eds) Networked Systems. NETYS 2021. Lecture Notes in Computer Science(), vol 12754. Springer, Cham. https://doi.org/10.1007/978-3-030-91014-3_6
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