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Meeting the deadline: on the complexity of fault-tolerant continuous gossip

Abstract

In this paper we introduce the problem of Continuous Gossip in which rumors are continually and dynamically injected throughout the network. Each rumor has a deadline, and the goal of a continuous gossip protocol is to ensure good “Quality of Delivery,” i.e., to deliver every rumor to every process before the deadline expires. Thus, a trivial solution to the problem of Continuous Gossip is simply for every process to broadcast every rumor as soon as it is injected. Unfortunately, this solution has high per-round message complexity. Complicating matters, we focus our attention on a highly dynamic network in which processes may continually crash and recover. In order to achieve good per-round message complexity in a dynamic network, processes need to continually form and re-form coalitions that cooperate to spread their rumors throughout the network. The key challenge for a Continuous Gossip protocol is the ongoing adaptation to the ever-changing set of active rumors and non-crashed process. In this work we show how to address this challenge; we develop randomized and deterministic protocols for Continuous Gossip and prove lower bounds on the per-round message-complexity, indicating that our protocols are close to optimal.

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References

  1. 1

    Aspnes J.: Spreading rumors rapidly despite an adversary. J. Algorithms 26, 386–411 (1998)

  2. 2

    Birman K.P., Hayden M., Ozkasap O., Xiao Z., Budiu M., Minsky Y.: Bimodal multicast. ACM Trans. Comput. Syst. 17(2), 41–86 (1999)

  3. 3

    Bollobas B., de la Vega W.F.: The diameter of random regular graphs. Combinatorica 2(2), 125–134 (1982)

  4. 4

    Boyd S., Ghosh A., Prabhakar B., Shah D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)

  5. 5

    Capalbo, M.R., Reingold, O., Vadhan, S.P., Wigderson, A.: Randomness conductors and constant-degree lossless expanders. In: STOC 2002, pp. 659–668 (2002)

  6. 6

    Chlebus B.S., Kowalski D.R.: Robust gossiping with an application to consensus. J. Comput. Syst. Sci. 72(8), 1262–1281 (2006)

  7. 7

    Chlebus, B.S., Kowalski, D.R.: Time and communication efficient consensus for crash failures. In: DISC 2006, pp. 314–328 (2006)

  8. 8

    Chlebus, B.S., Kowalski, D.R., Shvartsman, A.A.: Collective asynchronous reading with polylogarithmic worst-case overhead. In: STOC 2004, pp. 321–330 (2004)

  9. 9

    Demers, A., Greene, D., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H., Swinehart, D., Terry, D.: Epidemic algorithms for replicated database maintenance. In: PODC 1987, pp. 1–12 (1987)

  10. 10

    Diks K., Pelc A.: Optimal adaptive broadcasting with a bounded fraction of faulty nodes. Algorithmica 28(1), 37–50 (2000)

  11. 11

    Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: expanders, push vs pull, and robustness. In: ICALP 2009. pp. 366–377

  12. 12

    Eugster P., Guerraoui R., Handurukande S., Kermarrec A-M., Kouznetsov P.: Lightweight probabilistic broadcast. ACM Trans. Comput. Syst. 21(4), 341–374 (2003)

  13. 13

    Galil, Z., Mayer, A., Yung, M.: Resolving message complexity of Byzantine agreement and beyond. In: FOCS 1995, pp. 724–733 (1995)

  14. 14

    Georgiou, C., Gilbert, S., Guerraoui, R., Kowalski, D.R.: On the complexity of asynchronous gossip. In: PODC 2008, pp. 135–144 (2008)

  15. 15

    Georgiou C., Kowalski D.R., Shvartsman A.A.: Efficient gossip and robust distributed computation. Theor. Comput. Sci. 347(1-2), 130–166 (2005)

  16. 16

    Hromkovic J., Klasing R., Pelc A., Ruzika P., Unger W.: Dissemination of Information in Communications Networks: Broadcasting, Gossiping, Leader Election, and Fault-Tolerance. Springer, Berlin, Heidelberg (2005)

  17. 17

    Karp, R., Schindelhauer, C., Shenker, S., Vocking, B.: Randomized Rumor Spreading. In: FOCS 2000, pp. 565–574 (2000)

  18. 18

    Kempe D., Kleinberg J., Demers A.: Spatial gossip and resource location protocols. J. ACM 51, 943–967 (2004)

  19. 19

    Kermarrec A., Massoulie L., Ganesh A.: Probabilistic reliable dissemination in large-scale systems. IEEE Trans. Parallel Distrib. Syst. 14(3), 248–258 (2003)

  20. 20

    Kowalski, D.R., Strojnowski, M.: On the communication surplus incurred by faulty processors. In: DISC 2007, pp. 328–342 (2007)

  21. 21

    Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: STOC 2010, pp. 513–522 (2010)

  22. 22

    Pelc A.: Fault-tolerant broadcasting and gossiping in communication networks. Networks 28, 143–156 (1996)

  23. 23

    Pinsker, M.S.: On the complexity of a concentrator. In: Proceedings of 7th Annual Teletraffic Conference (1973)

  24. 24

    Pippenger N.: Sorting and selecting in rounds. SIAM J. Comput. 16, 1032–1038 (1987)

  25. 25

    Saks, M., Shavit, N., Woll, H.: Optimal time randomized consensus–making resilient algorithms fast in practice. In: SODA 1991, pp. 351–362 (1991)

  26. 26

    Ta-Shma, A., Umans, C., Zuckerman, D.: Loss-less condensers, unbalanced expanders, and extractors. In: STOC 2001, pp. 143–152 (2001)

  27. 27

    van Renesse, R., Minsky, Y., Hayden, M.: A gossip-style failure detection service. In: Proceedings of IFIP International Conference on Distributed Systems Platforms and Open Distributed Processing, pp. 55–70 (1998)

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Author information

Correspondence to Chryssis Georgiou.

Additional information

This work is supported by UCY (RA) CS-CG2011, NUS (FRC) R-252-000-443-133, and the Engineering and Physical Sciences Research Council [grant numbers EP/G023018/1, EP/H018816/1].

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Georgiou, C., Gilbert, S. & Kowalski, D.R. Meeting the deadline: on the complexity of fault-tolerant continuous gossip. Distrib. Comput. 24, 223–244 (2011). https://doi.org/10.1007/s00446-011-0144-6

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Keywords

  • Gossip
  • Crashes and restarts
  • Dynamic rumor injection
  • Random and expander graphs