On the wake-up problem in radio networks

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) = scriptOsign(k log k log n). Next we show an explicit construction of (n, g)-universal-synchronizers for g(k) = scriptOsign(k² polylog n). By way of applications, we obtain an existential wake-up algorithm which works in time scriptOsign(n log² n) and an explicitly instantiated algorithm that works in time scriptOsign(n Δ polylog n), where n is the number of nodes and Δ 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 scriptOsign(log n) than the underlying wake-up ones.