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Abstract:
We study the problem of waking up a collection of $n$ processors connected by a
multihop ad hoc ratio network with unknown topology, no access to a global
clock, and no collision detection mechanism available. Each node in the network
either wakes up spontaneously or gets activated by receiving a wake-up signal
from another node. All active nodes transmit the wake-up signals according to a
given protocol $\calW$. The running time of $\calW$ is the number of steps
counted from the first spontaneous wake-up until all nodes become activated. We
provide two protocols for this problem. The first one is a deterministic
protocol with running time $O(n^{5/3}\log n)$. Our protocol is based on a novel
concept of a shift-tolerant selector to which we refer as a (radio)
synchronizer. The second protocol is randomized, and its expected running time
is $O(D \log^2 n)$, where $D$ is the diameter of the network. Subsequently we
show how to employ our wake-up protocols to solve two other communication
primitives: leader election and clock synchronization.
