The Wake-Up Problem in Multi-Hop Radio Networks

We study the problem of waking up a collection of n processors connected by a multi-hop ad-hoc ratio network with unknown topology, no access to a global clock, and no collision detection mechanism available. Each node in the network wakes-up spontaneously, or it is activated by receiving a wake-up signal from another node. All active nodes transmit the wake-up signals according to a given protocol script Q sign. The running time of script Q sign 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 rotationtolerant selector to which we refer as a synchronizer. The second protocol is randomized, and its expected running time is O(D log² 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.