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Communication Complexity of Quasirandom Rumor Spreading

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Abstract

We consider rumor spreading on random graphs and hypercubes in the quasirandom phone call model. In this model, every node has a list of neighbors whose order is specified by an adversary. In step i every node opens a channel to its ith neighbor (modulo degree) on that list, beginning from a randomly chosen starting position. Then, the channels can be used for bi-directional communication in that step. The goal is to spread a message efficiently to all nodes of the graph.

For random graphs (with sufficiently many edges) we present an address-oblivious algorithm with runtime O(logn) that uses at most O(nloglogn) message transmissions. For hypercubes of dimension logn we present an address-oblivious algorithm with runtime O(logn) that uses at most O(n(loglogn)2) message transmissions.

Together with a result of Elsässer (Proc. of SPAA’06, pp. 148–157, 2006), our results imply that for random graphs the communication complexity of the quasirandom phone call model is significantly smaller than that of the standard phone call model.

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Notes

  1. W.h.p. or “with high probability” means with probability at least 1−n −c for some constant c>0.

References

  1. Berenbrink, P., Elsässer, R., Friedetzky, T.: Efficient randomised broadcasting in random regular networks with applications in peer-to-peer systems. In: Proc. of PODC’08, pp. 155–164 (2008)

    Google Scholar 

  2. Berenbrink, P., Elsässer, R., Sauerwald, T.: Randomised broadcasting: memory vs. randomness. In: Proc. of LATIN’10, pp. 306–319 (2010)

    Google Scholar 

  3. Berenbrink, P., Elsässer, R., Sauerwald, T.: Communication complexity of quasirandom rumor spreading. In: Proc. of ESA’10, pp. 134–145 (2010)

    Google Scholar 

  4. Bollobás, B.: Random Graphs. Academic Press, San Diego (1985)

    MATH  Google Scholar 

  5. Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost tight bounds for rumour spreading with conductance. In: Proc. of STOC’10, pp. 399–408 (2010)

    Google Scholar 

  6. 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: Proc. of PODC’87, pp. 1–12 (1987)

    Google Scholar 

  7. Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading. In: Proc. of SODA’08, pp. 773–781 (2008)

    Google Scholar 

  8. Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: expanders, push vs. pull, and robustness. In: Proc. of ICALP’09, pp. 366–377 (2009)

    Google Scholar 

  9. Elsässer, R.: On the communication complexity of randomized broadcasting in random-like graphs. In: Proc. of SPAA’06, pp. 148–157 (2006)

    Google Scholar 

  10. Elsässer, R., Sauerwald, T.: The power of memory in randomized broadcasting. In: Proc. of SODA’08, pp. 218–227 (2008)

    Google Scholar 

  11. Erdős, P., Rényi, A.: On random graphs I. Publ. Math. (Debr.) 6, 290–297 (1959)

    Google Scholar 

  12. Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Struct. Algorithms 1(4), 447–460 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fountoulakis, N., Huber, A., Panagiotou, K.: Reliable broadcasting in random networks and the effect of density. In: Proc. of INFOCOM’10, pp. 2552–2560 (2010)

    Google Scholar 

  14. Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Appl. Math. 10, 57–77 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  15. Giakkoupis, G.: Tight bounds for rumor spreading in graphs of a given conductance. In: Proc. of STACS’11, pp. 57–68 (2011)

    Google Scholar 

  16. Hagerup, T., Rüb, C.: A guided tour of Chernoff bounds. Inf. Process. Lett. 36(6), 305–308 (1990)

    Article  Google Scholar 

  17. Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: Proc. of FOCS’00, pp. 565–574 (2000)

    Google Scholar 

  18. McDiarmid, C.: On the method of bounded differences. In: Siemons, J. (ed.) Surveys in Combinatorics, 1989. London Mathematical Society Lectures Note Series, vol. 141, pp. 148–188. Cambridge University Press, Cambridge (1989)

    Chapter  Google Scholar 

  19. Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  20. Pittel, B.: On spreading a rumor. SIAM J. Appl. Math. 47(1), 213–223 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

We would like to thank the reviewers of this journal version for their helpful comments.

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Authors and Affiliations

  1. School of Computing Science, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Petra Berenbrink

  2. Department of Computer Science, University of Salzburg, Jakob-Haringer-Strasse 2, 5020, Salzburg, Austria

    Robert Elsässer

  3. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD, UK

    Thomas Sauerwald

Authors
  1. Petra Berenbrink
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  2. Robert Elsässer
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  3. Thomas Sauerwald
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Corresponding author

Correspondence to Thomas Sauerwald.

Additional information

An extended abstract of this paper appeared in the 18th Annual European Symposium (ESA’10) [3].

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Berenbrink, P., Elsässer, R. & Sauerwald, T. Communication Complexity of Quasirandom Rumor Spreading. Algorithmica 72, 467–492 (2015). https://doi.org/10.1007/s00453-013-9861-5

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