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

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 O(k log(1/b) k log n) time. We prove a lower bound that any deterministic algorithm requires Omega(k/b log n/k) time. We give a deterministic algorithm for the special case when b > dlog log n, for some constant d > 1, which wakes up the network in O(k/b log n log(b log n)) time. This algorithm misses time optimality by at most a factor of log n log b. We give a randomized algorithm that wakes up the network within O(k(1/b) ln 1/is an element of) rounds with the probability of at least 1 - is an element of, for any unknown 0 < is an element of < 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 O(log(-1) (1/p) k log n log(1/b) k) time with the probability of at least 1 - 1/poly(n).