The wake-up problem in multi-hop radio networks.pdfVIP

The Wake-Up Problem in Multi-Hop Radio Networks Marek Chrobak Leszek Ga?sieniec
Dariusz Kowalski  Abstract We study the problem of waking up a collection of  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  . The running time of  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    . Our protocol is based on a novel concept of a rotation- tolerant selector to which we refer as a synchronizer. The second protocol is randomized, and its expected running time is  , where  is the diameter of the network. Subsequently we show how to employ our wake-up pro- tocols to solve two other communication primitives: leader election and clock synchronization. 1 Introduction We define an ad-hoc multi-hop radio network as a directed, strongly-connected graph with  vertices, whose nodes rep- resent processors and outgoing edges represent their trans- mission ranges. The execution time is divided into discrete time steps, same for all processors. We assume that each pro- cessor is assigned a unique integer identifier from a range of size  . The processors know the range of the identifiers, but they do not know the network’s topology. We consider the fundamental problem of waking up the processors of an ad-hoc multi-hop radio network. Initially, all nodes are assumed to be asleep. Each node in the network can wake-up spontaneously, or can be activated by receiving  Department of Computer Science, University of California, Riverside, CA 92521, USA. Research supported by NSF grants CCR-9