Continuous Aggregation in Dynamic Ad-Hoc Networks

  • Sebastian Abshoff
  • Friedhelm Meyer auf der Heide
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8576)


We study a scenario in which n nodes of a mobile ad-hoc network continuously collect data. Their task is to repeatedly update aggregated information about the data, e.g., the maximum, the sum, or the full information about all data received by all nodes at a given time step. This aggregated information has to be disseminated to all nodes.

We propose two performance measures for distributed algorithms for these tasks: The delay is the maximum time needed until the aggregated information about the data measured at some time is output at all nodes. We assume that a node can broadcast information proportional to a constant number of data items per round. A too large communication volume needed for producing an output can lead to the effect that the delay grows unboundedly over time. Thus, we have to cope with the restriction that outputs are computed not for all but only for a fraction of rounds. We refer to this fraction as the output rate of the algorithm.

Our main technical contributions are trade-offs between delay and output rate for aggregation problems under the assumption of T-stable dynamics in the mobile ad-hoc network: The network is always connected and is stable for time intervals of length Open image in new window where Open image in new window is the time needed to compute a maximal independent set. For the maximum function, we are able to show that we can achieve an output rate of Open image in new window with delay Open image in new window . For the sum, we show that it is possible to achieve an output rate of Open image in new window with delay Open image in new window if Open image in new window , and if Open image in new window , we can achieve an output rate of Open image in new window with delay Open image in new window .


Dynamic Networks Aggregation Token Dissemination 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abshoff, S., Benter, M., Cord-Landwehr, A., Malatyali, M., Meyer auf der Heide, F.: Token dissemination in geometric dynamic networks. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds.) ALGOSENSORS 2013. LNCS, vol. 8243, pp. 22–34. Springer, Heidelberg (2014)Google Scholar
  2. 2.
    Abshoff, S., Benter, M., Malatyali, M., Meyer auf der Heide, F.: On two-party communication through dynamic networks. In: Baldoni, R., Nisse, N., van Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 11–22. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election and related problems (detailed summary). In: Aho, A.V. (ed.) STOC, pp. 230–240. ACM (1987)Google Scholar
  4. 4.
    Chaudhuri, S., Dubhashi, D.P.: Probabilistic recurrence relations revisited. Theor. Comput. Sci. 181(1), 45–56 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Cornejo, A., Gilbert, S., Newport, C.C.: Aggregation in dynamic networks. In: Kowalski, D., Panconesi, A. (eds.) PODC, pp. 195–204. ACM (2012)Google Scholar
  6. 6.
    Dutta, C., Pandurangan, G., Rajaraman, R., Sun, Z., Viola, E.: On the complexity of information spreading in dynamic networks. In: Khanna, S. (ed.) SODA, pp. 717–736. SIAM (2013)Google Scholar
  7. 7.
    Haeupler, B., Karger, D.R.: Faster information dissemination in dynamic networks via network coding. In: Gavoille, C., Fraigniaud, P. (eds.) PODC, pp. 381–390. ACM (2011)Google Scholar
  8. 8.
    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
  9. 9.
    Karp, R.M.: Probabilistic recurrence relations. J. ACM 41(6), 1136–1150 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Kuhn, F., Locher, T., Schmid, S.: Distributed computation of the mode. In: Bazzi, R.A., Patt-Shamir, B. (eds.) PODC, pp. 15–24. ACM (2008)Google Scholar
  11. 11.
    Kuhn, F., Locher, T., Wattenhofer, R.: Tight bounds for distributed selection. In: Gibbons, P.B., Scheideler, C. (eds.) SPAA, pp. 145–153. ACM (2007)Google Scholar
  12. 12.
    Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: Schulman, L.J. (ed.) STOC, pp. 513–522. ACM (2010)Google Scholar
  13. 13.
    Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21(1), 193–201 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15(4), 1036–1053 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Mosk-Aoyama, D., Shah, D.: Computing separable functions via gossip. In: Ruppert, E., Malkhi, D. (eds.) PODC, pp. 113–122. ACM (2006)Google Scholar
  16. 16.
    Panconesi, A., Srinivasan, A.: Improved distributed algorithms for coloring and network decomposition problems. In: Kosaraju, S.R., Fellows, M., Wigderson, A., Ellis, J.A. (eds.) STOC, pp. 581–592. ACM (1992)Google Scholar
  17. 17.
    Schneider, J., Wattenhofer, R.: A log-star distributed maximal independent set algorithm for growth-bounded graphs. In: Bazzi, R.A., Patt-Shamir, B. (eds.) PODC, pp. 35–44. ACM (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sebastian Abshoff
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  1. 1.Heinz Nixdorf Institute & Computer Science DepartmentUniversity of PaderbornPaderbornGermany

Personalised recommendations