Information Spreading in Dynamic Networks Under Oblivious Adversaries

  • John Augustine
  • Chen Avin
  • Mehraneh Liaee
  • Gopal Pandurangan
  • Rajmohan Rajaraman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)

Abstract

We study the problem of gossip in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, there are n tokens arbitrarily distributed among the n network nodes, and the goal is to disseminate all the n tokens to every node. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. An important open question is whether gossip can be realized by a distributed protocol that can do significantly better than an easily achievable bound of \(O(n^2)\) rounds.

In this paper, we study oblivious adversaries, i.e., those that are oblivious to the random choices made by the protocol. We consider Rand-Diff, a natural distributed algorithm in which neighbors exchange a token chosen uniformly at random from the difference of their token sets. We present an \(\tilde{\varOmega }(n^{3/2})\) lower bound for Rand-Diff under an oblivious adversary. We also present an \(\tilde{\varOmega }(n^{4/3})\) lower bound under a stronger notion of oblivious adversary for a class of randomized distributed algorithms—symmetric knowledge-based algorithms— in which nodes make token transmission decisions based entirely on the sets of tokens they possess over time. On the positive side, we present a centralized algorithm that completes gossip in \(\tilde{O}(n^{3/2})\) rounds with high probability, under any oblivious adversary. We also show an \(\tilde{O}(n^{5/3})\) upper bound for Rand-Diff in a restricted class of oblivious adversaries, which we call paths-respecting, that may be of independent interest.

References

  1. 1.
    Augustine, J., Pandurangan, G., Robinson, P., Upfal, E.: Towards robust and efficient computation in dynamic peer-to-peer networks. In: SODA, pp. 551–569 (2012)Google Scholar
  2. 2.
    Augustine, J., Avin, C., Liaee, M., Pandurangan, G., Rajaraman, R.: Information spreading in dynamic networks under oblivious adversaries (2016). arXiv:1603.06109
  3. 3.
    Augustine, J., Molla, A.R., Morsy, E., Pandurangan, G., Robinson, P., Upfal, E.: Storage and search in dynamic peer-to-peer networks. In: SPAA, pp. 53–62 (2013)Google Scholar
  4. 4.
    Augustine, J., Pandurangan, G., Robinson, P.: Fast byzantine agreement in dynamic networks. In: PODC, pp. 74–83 (2013)Google Scholar
  5. 5.
    Augustine, J., Pandurangan, G., Robinson, P., Roche, S., Upfal, E.: Enabling robust and efficient distributed computation in dynamic peer-to-peer networks. In: FOCS, pp. 350–369 (2015)Google Scholar
  6. 6.
    Avin, C., Koucký, M., Lotker, Z.: How to explore a fast-changing world (cover time of a simple random walk on evolving graphs). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 121–132. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Baumann, H., Crescenzi, P., Fraigniaud, P.: Parsimonious flooding in dynamic graphs. In: PODC, pp. 260–269 (2009)Google Scholar
  8. 8.
    Baumann, H., Crescenzi, P., Fraigniaud, P.: Parsimonious flooding in dynamic graphs. Distrib. Comput. 24(1), 31–44 (2011)CrossRefMATHGoogle Scholar
  9. 9.
    Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24(1), 5–34 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(1–6), 309–320 (2000)CrossRefGoogle Scholar
  11. 11.
    Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)CrossRefGoogle Scholar
  12. 12.
    Clementi, A.E.F., Monti, A., Pasquale, F., Silvestri, R.: Broadcasting in dynamic radio networks. J. Comput. Syst. Sci. 75(4), 213–230 (2009)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Clementi, A.E.F., Macci, C., Monti, A., Pasquale, F., Silvestri, R.: Flooding time in edge-markovian dynamic graphs. In: PODC, pp. 213–222 (2008)Google Scholar
  14. 14.
    Cooper, C., Frieze, A.: Crawling on simple models of web graphs. Internet Math. 1, 57–90 (2003)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Ferreira, A.: Building a reference combinatorial model for manets. IEEE Netw. 18(5), 24–29 (2004)CrossRefGoogle Scholar
  17. 17.
    Ferreira, A., Goldman, A., Monteiro, J.: On the evaluation of shortest journeys in dynamic networks. In: NCA, pp. 3–10 (2007)Google Scholar
  18. 18.
    Flaxman, A., Frieze, A.M., Upfal, E.: Efficient communication in an ad-hoc network. J. Algorithms 52(1), 1–7 (2004)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Georgiou, C., Gilbert, S., Guerraoui, R., Kowalski, D.R.: On the complexity of asynchronous gossip. In: PODC, pp. 135–144 (2008)Google Scholar
  20. 20.
    Gurevich, M., Keidar, I.: Correctness of gossip-based membership under message loss. In: PODC, pp. 151–160 (2009)Google Scholar
  21. 21.
    Haeupler, B.: Analyzing network coding gossip made easy. In: STOC, pp. 293–302 (2011)Google Scholar
  22. 22.
    Haeupler, B., Karger, D.: Faster information dissemination in dynamic networks via network coding. In: PODC, pp. 381–390 (2011)Google Scholar
  23. 23.
    Haeupler, B., Kuhn, F.: Lower bounds on information dissemination in dynamic networks. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 166–180. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Jarry, A., Lotker, Z.: Connectivity in evolving graph with geometric properties. In: DIALM-POMC, pp. 24–30 (2004)Google Scholar
  25. 25.
    Kempe, D., Kleinberg, J., Kumar, A.: Connectivity and inference problems for temporal networks. JCSS 64(4), 820–842 (2002)MathSciNetMATHGoogle Scholar
  26. 26.
    Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522 (2010)Google Scholar
  27. 27.
    Kuhn, F., Oshman, R., Moses, Y.: Coordinated consensus in dynamic networks. In: PODC, pp. 1–10 (2011)Google Scholar
  28. 28.
    Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, and Hypercubes. Morgan-Kaufmann (1991)Google Scholar
  29. 29.
    Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. PNAS 102(33), 11623–11628 (2005)CrossRefGoogle Scholar
  30. 30.
    O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: DIALM-POMC, pp. 104–110 (2005)Google Scholar
  31. 31.
    Pandurangan, G.: Distributed algorithmic foundations of dynamic networks. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 18–22. Springer, Heidelberg (2014)Google Scholar
  32. 32.
    Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM (2000)Google Scholar
  33. 33.
    Das Sarma, A., Molla, A.R., Pandurangan, G.: Fast distributed computation in dynamic networks via random walks. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 136–150. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  34. 34.
    Sarwate, A.D., Dimakis, A.G.: The impact of mobility on gossip algorithms. In: INFOCOM, pp. 2088–2096 (2009)Google Scholar
  35. 35.
    Topkis, D.M.: Concurrent broadcast for information dissemination. IEEE Trans. Soft. Eng. 11, 1107–1112 (1985)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • John Augustine
    • 1
  • Chen Avin
    • 2
  • Mehraneh Liaee
    • 3
  • Gopal Pandurangan
    • 4
  • Rajmohan Rajaraman
    • 3
  1. 1.IIT MadrasChennaiIndia
  2. 2.Ben-Gurion University of the NegevBeershebaIsrael
  3. 3.Northeastern UniversityBostonUSA
  4. 4.University of HoustonHoustonUSA

Personalised recommendations