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.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901), by the EU within FET project MULTIPLEX under contract no. 317532, and the International Graduate School “Dynamic Intelligent Systems”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
To upper bound the worst-case traveling distance for a fixed node pair \(u\) and \(v\), we can w.l.o.g. assume that \(u\) is static while \(v\) moves with velocity of at most \(2v_{\max }\).
- 2.
Note that \(n\) is not known by the nodes beforehand but as described by Kuhn et al. [10] it can be determined involving the dissemination procedure itself using different estimates for \(n\).
References
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)
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)
Boyd, S.P., Ghosh, A., Prabhakar, B., Shah, D.: Gossip algorithms: design, analysis and applications. In: INFOCOM, pp. 1653–1664 (2005)
Brandes, P., Meyer auf der Heide, F.: Distributed computing in fault-prone dynamic networks. In: TADDS, pp. 9–14 (2012)
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)
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)
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)
Haeupler, B., Karger, D.R.: Faster information dissemination in dynamic networks via network coding. In: PODC, pp. 381–390 (2011)
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)
Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522 (2010)
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)
Kuhn, F., Oshman, R.: Dynamic networks: models and algorithms. SIGACT News 42(1), 82–96 (2011)
Kuhn, F., Wattenhofer, R., Zollinger, A.: Worst-case optimal and average-case efficient geometric ad-hoc routing. In: MobiHoc, pp. 267–278 (2003)
Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric ad-hoc routing: of theory and practice. In: PODC, pp. 63–72 (2003)
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)
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)
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 2012
O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: DIALM-POMC, pp. 104–110 (2005)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abshoff, S., Benter, M., Cord-Landwehr, A., Malatyali, M., Meyer auf der Heide, F. (2014). Token Dissemination in Geometric Dynamic Networks. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-45346-5_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45345-8
Online ISBN: 978-3-642-45346-5
eBook Packages: Computer ScienceComputer Science (R0)