Abstract
One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following robust, simple, and scalable randomized broadcasting protocol: At some time t an information is placed at one of the nodes of a graph G, and in the succeeding steps, each informed node choses one of its neighbors in G uniformly at random, and sends the information to this neighbor. We show that this algorithm spreads an information to all nodes in a Star graph S n of dimension n within O(log (N)) steps, with high probability, where N denotes the number of nodes in S n . In our proofs, we apply some methods which may be of independent interest, and extend the results of [10] concerning randomized broadcasting in hypercubic graphs.
This work was partially supported by the German Research Foundation (DFG) within the SFB 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and by the EU within the 6th Framework Programme under contract 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS).
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Elsässer, R., Sauerwald, T. (2005). On Randomized Broadcasting in Star Graphs. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_27
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DOI: https://doi.org/10.1007/11604686_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
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