Abstract
We study the time complexity of single and multi token broadcast in adversarial dynamic radio networks. Initially, k tokens (which are k pieces of information) are distributed among the n nodes of a network and all the tokens need to be disseminated to all the nodes in the network. We first consider the single-token broadcast problem (i.e., the case k=1). By presenting upper and lower bounds, we show that the time complexity of single-token broadcast depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. Then, we give two generic algorithms which allow to transform generalized forms of single-token broadcast algorithms into multi-token broadcast (k-token broadcast) algorithms. Based on these generic algorithms, we obtain k-token broadcast algorithms for a number of different dynamic network settings. For one of the modeling assumptions, our algorithm is complemented by a lower bound which shows that the upper bound is close to optimal.
Highlights
A rich theory on algorithms for large-scale wireless networks exists and we have a rather precise understanding of the complexity of many basic computation and communicationLeibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany 7:2The Cost of Global Broadcast in Dynamic Radio Networks tasks for a variety of wireless network models
For a 1-oblivious adversary, we show that even for any T ≤ (n/k)1−ε and for any k ≥ 1, global broadcast in T -interval k-connected networks requires at least Ω(n2/k2 log n) time
Most of the existing work is based on static networks and on communication models where wireless signal reception is modeled in a completely deterministic way
Summary
A rich theory on algorithms for large-scale wireless networks exists and we have a rather precise understanding of the complexity of many basic computation and communication. In [11], it is shown that in 1-interval 1-connected networks (i.e., the graph is connected in every round), the complexity of global broadcast for a 1-oblivious adversary is Θ(n2/ log n). In [13], it is shown that when only assuming an ∞-oblivious adversary, the running time can be improved to O((D + log n) log n), where D is the diameter of the stable connected subgraph Note that in this case, the algorithm in [13] achieves essentially the same time complexity as is possible in static graphs of diameter D [5, 20, 23].
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