Scalable Wake-up of Multi-channel Single-Hop Radio Networks

Abstract

We consider waking up a single-hop radio network with multiple channels. There are n stations connected to b channels without collision detection. Some k stations may become active spontaneously at arbitrary times, where k is unknown, and the goal is for all the stations to hear a successful transmission as soon as possible after the first spontaneous activation. We present a deterministic algorithm for the general problem that wakes up the network in ${\mathcal O}(k\log^{1/b} k\log n)$ time. We prove a lower bound that any deterministic algorithm requires $\Omega(\frac{k}{b}\log \frac{n}{k})$ time. We give a deterministic algorithm for the special case when b > d loglogn, for some constant d > 1, which wakes up the network in ${\mathcal O}(\frac{k}{b}\log n\log(b\log n))$ time. This algorithm misses time optimality by at most a factor of lognlogb. We give a randomized algorithm that wakes up the network within ${\mathcal O}(k^{1/b}\ln \frac{1}{\epsilon})$ rounds with the probability of at least 1 − ε, for any unknown 0 < ε < 1. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability p, independently across all channels and rounds. For this model, we give a deterministic algorithm that wakes up the network in ${\mathcal O}(\log^{-1}(1/p) k\log n\log^{1/b} k)$ time with the probability of at least 1 − 1/poly(n).