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Token Dissemination in Geometric Dynamic Networks

  • Sebastian AbshoffEmail author
  • Markus Benter
  • Andreas Cord-Landwehr
  • Manuel Malatyali
  • Friedhelm Meyer auf der Heide
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8243)

Abstract

We consider the \(k\)-token dissemination problem, where \(k\) initially arbitrarily distributed tokens have to be disseminated to all nodes in a dynamic network (as introduced by Kuhn et al. STOC 2010). In contrast to general dynamic networks, our dynamic networks are unit disk graphs, i.e., nodes are embedded into the Euclidean plane and two nodes are connected if and only if their distance is at most \(R\). Our worst-case adversary is allowed to move the nodes on the plane, but the maximum velocity \(v_{\max }\) of each node is limited and the graph must be connected in each round. For this model, we provide almost tight lower and upper bounds for \(k\)-token dissemination if nodes are restricted to send only one token per round. It turns out that the maximum velocity \(v_{\max }\) is a meaningful parameter to characterize dynamics in our model.

Keywords

Geometric dynamic networks Token dissemination  Distributed computing 

References

  1. 1.
    Bienkowski, M., Byrka, J., Korzeniowski, M., Meyer auf der Heide, F.: Optimal algorithms for page migration in dynamic networks. J. Discrete Algorithms 7(4), 545–569 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Analysis and optimization of randomized gossip algorithms. In: 43rd IEEE Conference on Decision and Control, 2004. CDC, vol. 5, pp. 5310–5315 (2004)Google Scholar
  3. 3.
    Boyd, S.P., Ghosh, A., Prabhakar, B., Shah, D.: Gossip algorithms: design, analysis and applications. In: INFOCOM, pp. 1653–1664 (2005)Google Scholar
  4. 4.
    Brandes, P., Meyer auf der Heide, F.: Distributed computing in fault-prone dynamic networks. In: TADDS, pp. 9–14 (2012)Google Scholar
  5. 5.
    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
  6. 6.
    Dimakis, A.G., Sarwate, A.D., Wainwright, M.J.: Geographic gossip: Efficient averaging for sensor networks. IEEE Trans. Sig. Process. 56(3), 1205–1216 (2008)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hannes, F., Stefan, R., Ivan, S.: Routing in wireless sensor networks. In: Misra, S., Woungang, I., Misra, S.C. (eds.) Guide to Wireless Sensor Networks, pp. 81–111. Springer, London (2009)Google Scholar
  8. 8.
    Haeupler, B., Karger, D.R.: Faster information dissemination in dynamic networks via network coding. In: PODC, pp. 381–390 (2011)Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522 (2010)Google Scholar
  11. 11.
    Kempkes, B., Meyer auf der Heide, F.: Local, self-organizing strategies for robotic formation problems. In: Erlebach, T., Nikoletseas, S., Orponen, P. (eds.) ALGOSENSORS 2011. LNCS, vol. 7111, pp. 4–12. Springer, Heidelberg (2012)Google Scholar
  12. 12.
    Kuhn, F., Oshman, R.: Dynamic networks: models and algorithms. SIGACT News 42(1), 82–96 (2011)CrossRefGoogle Scholar
  13. 13.
    Kuhn, F., Wattenhofer, R., Zollinger, A.: Worst-case optimal and average-case efficient geometric ad-hoc routing. In: MobiHoc, pp. 267–278 (2003)Google Scholar
  14. 14.
    Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric ad-hoc routing: of theory and practice. In: PODC, pp. 63–72 (2003)Google Scholar
  15. 15.
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Brief announcement: naming and counting in anonymous unknown dynamic betworks. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 437–438. Springer, Heidelberg (2012)Google Scholar
  16. 16.
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Causality, influence, and computation in possibly disconnected synchronous dynamic networks. In: Baldoni, R., Flocchini, P., Binoy, R. (eds.) OPODIS 2012. LNCS, vol. 7702, pp. 269–283. Springer, Heidelberg (2012)Google Scholar
  17. 17.
    Oshman, R.: Distributed computation in wireless and dynamic networks. Ph.D. thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, September 2012Google Scholar
  18. 18.
    O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: DIALM-POMC, pp. 104–110 (2005)Google Scholar
  19. 19.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sebastian Abshoff
    • 1
    Email author
  • Markus Benter
    • 1
  • Andreas Cord-Landwehr
    • 1
  • Manuel Malatyali
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  1. 1.Heinz Nixdorf Institute & Computer Science DepartmentUniversity of PaderbornPaderbornGermany

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