Advertisement

Parsimonious Flooding in Geometric Random-Walks

(Extended Abstract)
  • Andrea E. F. Clementi
  • Riccardo Silvestri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6950)

Abstract

We study the information spreading yielded by the (Parsimonious) k-Flooding Protocol in geometric Mobile Ad-Hoc Networks. We consider n agents on a square of side length L performing independent random walks with move radius ρ. At any time step, every active agent v informs every non-informed agent which is within distance R from v (R > 0 is the transmission radius). An agent is only active for the next k time steps following the one in which has been informed and, after that, she is removed. At the initial time step, a source agent is informed and we look at the completion time of the protocol, i.e., the first time step (if any) in which all agents are informed.

The presence of removed agents makes this process much more complex than the (standard) flooding and no analytical results are available over any explicit mobility model.

We prove optimal bounds on the completion time depending on the parameters n, L, R, and ρ. The obtained bounds hold with high probability. Our method of analysis provides a clear picture of the dynamic shape of the information spreading (or infection wave) over the time.

Keywords

Completion Time Infection Process Transmission Radius Information Spreading White Agent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ball, F., Neal, P.: A general model for stochastic SIR epidemics with two levels of mixing. Math. Biosci. 180, 73–102 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ball, F., Neal, P.: Network epidemic models with two levels of mixing. Math. Biosci. 212, 69–87 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baumann, H., Crescenzi, P., Fraigniaud, P.: Parsimonious flooding in dynamic graphs. In: Proc. of the 28th ACM PODC 2009 (2009)Google Scholar
  4. 4.
    Brauer, N., van den Driessche, P., Wu, J. (eds.): Mathematical Epidemiology. Lecture Notes in Mathematics, subseries in Mathematical Biosciences, 1945 (2008)Google Scholar
  5. 5.
    Clementi, A., Monti, A., Pasquale, F., Silvestri, R.: Broadcasting in dynamic radio networks. J. Comput. Syst. Sci. 75(4) (2009); (preliminary version in ACM PODC 2007)Google Scholar
  6. 6.
    Clementi, A., Macci, C., Monti, A., Pasquale, F., Silvestri, R.: Flooding time in edge-Markovian dynamic graphs. In: Proc of the 27th ACM PODC 2008 (2008)Google Scholar
  7. 7.
    Clementi, A., Monti, A., Pasquale, F., Silvestri, R.: Information spreading in stationary markovian evolving graphs. In: Proc. of the 23rd IEEE IPDPS 2009 (2009)Google Scholar
  8. 8.
    Clementi, A., Pasquale, F., Silvestri, R.: Manets: High mobility can make up for low transmission power. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 387–398. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Clementi, A., Monti, A., Silvestri, R.: Flooding over Manhattan. In: Proc of the 29th ACM PODC 2010 (2010)Google Scholar
  10. 10.
    Clementi, A., Silvestri, R.: Parsimonious Flooding in Geometric Random-Walks, ArXiv e-prints, 2011arXiv1101.5308C (2011)Google Scholar
  11. 11.
    Diaz, J., Mitsche, D., Perez-Gimenez, X.: On the connectivity of dynamic random geometric graphs. In: Proc. of 19th Annual ACM-SIAM SODA 2008, pp. 601–610 (2008)Google Scholar
  12. 12.
    Grossglauser, M., Tse, N.C.: Mobility increases the capacity of ad-hoc wireless networks. IEEE/ACM Trans. on Networking 10(4) (2002)Google Scholar
  13. 13.
    Jacquet, P., Mans, B., Rodolakis, G.: Information propagation speed in mobile and delay tolerant networks. In: Proc. of 29th IEEE INFOCOM 2009, pp. 244–252. IEEE, Los Alamitos (2009)Google Scholar
  14. 14.
    Kong, Z., Yeh, E.M.: On the latency for information dissemination in mobile wireless networks. In: Proc. of 9th ACM MobiHoc 2008, pp. 139–148 (2008)Google Scholar
  15. 15.
    Le Boudec, J.Y., Vojnovic, M.: The random trip model: stability, stationary regime, and perfect simulation. IEEE/ACM Trans. Netw. 14(6), 1153–1166 (2006)CrossRefGoogle Scholar
  16. 16.
    McDiarmid, C.: On the method of bounded differences. In: Siemons, J. (ed.) London Mathematical Society Lecture Note, vol. 141, pp. 148–188. Cambridge University Press, Cambridge (1989)Google Scholar
  17. 17.
    Peres, Y., Sinclair, A., Sousi, P., Stauffer, A.: Mobile Geometric Graphs: Detection, Coverage and Percolation Eprint arXiv:1008.0075v2) (to appear in ACM SODA 2011) (2010)Google Scholar
  18. 18.
    Pettarin, A., Pietracaprina, A., Pucci, G., Upfal, E.: Infectious Random Walks. Eprint arXiv:1007.1604 (2010), Extended abstract will appear in (ACM PODC 2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrea E. F. Clementi
    • 1
  • Riccardo Silvestri
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”Italy
  2. 2.Dipartimento di InformaticaUniversità di Roma “La Sapienza”Italy

Personalised recommendations