Abstract
Radio networks model wireless communication when processing units communicate using one wave frequency. This is captured by the property that multiple messages arriving simultaneously to a node interfere with one another and none of them can be read reliably. We present improved solutions to the problem of waking up such a network. This requires activating all nodes in a scenario when some nodes start to be active spontaneously, while every sleeping node needs to be awaken by receiving successfully a message from a neighbor. Our contributions concern the existence and efficient construction of universal radio synchronizers, which are combinatorial structures introduced in [6] as building blocks of efficient wake-up algorithms. First we show by counting that there are (n,g)-universal synchronizers for \(g(k)={\mathcal O}(k \ {\rm log}\ k \ {\rm log}\ n)\). Next we show an explicit construction of (n,g)-universal-synchronizers for \(g(k) = {\mathcal O}(k^{2}{\rm polylog}\ n)\). By way of applications, we obtain an existential wake-up algorithm which works in time \({\mathcal O}(n {\rm log}^{2}n)\) and an explicitly instantiated algorithm that works in time \({\mathcal O}(n{\it \Delta} {\rm polylog}\ n)\), where n is the number of nodes and \({\it \Delta}\) is the maximum in-degree in the network. Algorithms for leader-election and synchronization can be developed on top of wake-up ones, as shown in [7], such that they work in time slower by a factor of \({\mathcal O}({\rm log} \ n)\) than the underlying wake-up ones.
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Chlebus, B.S., Gąsieniec, L., Kowalski, D.R., Radzik, T. (2005). On the Wake-Up Problem in Radio Networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_29
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DOI: https://doi.org/10.1007/11523468_29
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