Adaptive Rumor Spreading
Abstract
Motivated by the recent emergence of the so-called opportunistic communication networks, we consider the issue of adaptivity in the most basic continuous time (asynchronous) rumor spreading process. In our setting a rumor has to be spread to a population; the service provider can push it at any time to any node in the network and has unit cost for doing this. On the other hand, as usual in rumor spreading, nodes share the rumor upon meeting and this imposes no cost on the service provider. Rather than fixing a budget on the number of pushes, we consider the cost version of the problem with a fixed deadline and ask for a minimum cost strategy that spreads the rumor to every node. A non-adaptive strategy can only intervene at the beginning and at the end, while an adaptive strategy has full knowledge and intervention capabilities. Our main result is that in the homogeneous case (where every pair of nodes randomly meet at the same rate) the benefit of adaptivity is bounded by a constant. This requires a subtle analysis of the underlying random process that is of interest in its own right.
Notes
Acknowledgments
We thank Albert Banchs, Antonio Fernández, Domenico Giustiniano, Nicole Immorlica, Julia Komjáthy, Brendan Lucier, and Yaron Singer for stimulating discussions and helpful pointers to the literature.
References
- 1.Andersson, H., Britton, T.: Stochastic Epidemic Models and Their Statistical Analysis. Lecture Notes in Statistics. Springer, New York (2000)CrossRefMATHGoogle Scholar
- 2.Asadpour, A., Nazerzadeh, H., Saberi, A.: Stochastic submodular maximization. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 477–489. Springer, Heidelberg (2008) CrossRefGoogle Scholar
- 3.Bailey, N.: A simple stochastic epidemic. Biometrika 37, 193–202 (1950)MathSciNetCrossRefMATHGoogle Scholar
- 4.Barry, K.: Ford bets the fiesta on social networking, September 2009. www.wired.com/2009/04/how-the-fiesta/
- 5.Bartlett, M.: An Introduction to Stochastic Processes, with Special Reference to Methods and Applications. Cambridge University Press, Cambridge (1978) MATHGoogle Scholar
- 6.Bollobás, B., Kohayakawa, Y.: On Richardson’s model on the hypercube. In: Bollobás, B., Thomason, A. (eds.) Combinatorics, Geometry and Probability. Cambridge University Press, Cambridge (1997) CrossRefGoogle Scholar
- 7.Borgs, C., Brautbar, M., Chayes, J., Lucier, B.: Maximizing social influence in nearly optimal time. In: SODA (2014)Google Scholar
- 8.Boyd, S., Arpita, G., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52(6), 2508–2530 (2006)MathSciNetCrossRefMATHGoogle Scholar
- 9.Chen, N.: On the approximability of influence in social networks. In: SODA (2008)Google Scholar
- 10.Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: KDD (2010)Google Scholar
- 11.Chen, Y., Krause, A.: Near-optimal batch mode active learning and adaptive submodular optimization. In: ICML (2013)Google Scholar
- 12.Cisco: VNI: Global mobile data traffic forecast update, 2013–2018 (2014). www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white_paper_c11-520862.html. Accessed 28 October 2014
- 13.Doerr, B., Künnemann, M.: Tight analysis of randomized rumor spreading in complete graphs. In: ANALCO (2014)Google Scholar
- 14.Domingos, P., Richardson, M.: Mining the network value customers. In: KDD (2001)Google Scholar
- 15.Golovin, D., Krause, A.: Adaptive submodularity: theory and applications in active learning and stochastic optimization. J. Artif. Intell. Res. 42, 427–486 (2011)MathSciNetMATHGoogle Scholar
- 16.Grimmett, G.: Probability on Graphs: Random Processes on Graphs and Lattices. Cambridge University Press, Cambridge (2010). Institute of Mathematical Statistics Textbooks CrossRefMATHGoogle Scholar
- 17.Han, B., Hui, P., Kumar, A., Marathe, M., Pei, G., Srinivasan, A.: Cellular traffic offloading through opportunistic communications: a case study. In: CHANTS (2010)Google Scholar
- 18.Horel, T., Singer, Y.: Scalable methods for adaptively seeding a social network. In: WWW (2015)Google Scholar
- 19.Ioannidis, S., Chaintreau, A., Massoulie, L.: Optimal and scalable distribution of content updates over a mobile social network. In: IEEE INFOCOM (2009)Google Scholar
- 20.Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: SIGKDD (2003)Google Scholar
- 21.Kempe, D., Kleinberg, J., Tardos, E.: Influential nodes in a diffusion model. In: ICALP (2005)Google Scholar
- 22.Kleinberg, J.: Cascading behavior in social and economic networks. In: ACM EC (2013)Google Scholar
- 23.Sciancalepore, V., Giustiniano, D., Banchs, A., Picu, A.: Offloading cellular traffic through opportunistic communications: analysis and optimization. ArXiv preprint 1405.3548 (2014)
- 24.Seeman, L., Singer, Y.: Adaptive seeding in social networks. In: FOCS (2013)Google Scholar
- 25.Whitbeck, J., Amorim, M., Lopez, Y., Leguay, J., Conan, V.: Relieving the wireless infrastructure: When opportunistic networks meet guaranteed delays. In: WOWMOM (2011)Google Scholar
Copyright information
Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.