Abstract
We consider the problem of deterministic broadcasting in undirected radio networks with limited topological information. We show that for every deterministic protocol there exists a radius 2 network which requires at least \(\Omega(n^{\frac{1}{2}})\) rounds for completing broadcast. The previous best lower bound for constant diameter networks is \(\Omega(n^{\frac{1}{4}})\) rounds, due to [23]. For networks of radius D the lower bound can be extended to \(\Omega((nD)^{\frac{1}{2}})\) rounds. This resolves the open problem posed by [23].
Of perhaps more interest is our approach for proving the lower bound which is novel. We quantify the amount of connectivity information, about the topology of the network, that the source can learn in arbitrary number of rounds of an a deterministic broadcasting protocol. This approach is much more intuitive and exposes the structure of the broadcasting problem. We believe it is of independent interest and may have other applications.
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Brito, C., Gafni, E., Vaya, S. (2004). An Information Theoretic Lower Bound for Broadcasting in Radio Networks. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_47
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