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”.
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- 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 \(n\).
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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
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DOI: https://doi.org/10.1007/978-3-642-45346-5_3
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