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 O(k log1/b k log n) time. We prove a lower bound that any deterministic algorithm requires Ω(Formula Presented) 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(Formula Presented) 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(Formula Presented) rounds with the probability of at least 1 - ɛ, for any unknown 0 < ɛ < 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 log1/b k) time with the probability of at least 1 - 1/poly(n).