Eficient communication in unknown networks

Abstract

We consider the problem of disseminating messages in net- works. We are interested in information dissemination algorithms in which machines operate independently without any knowledge of the network topology or size. Three communication tasks of increasing dif- ficulty are studied. In blind broadcasting (BB) the goal is to communi- cate the source message to all nodes. In acknowledged blind broadcasting (ABB) the goal is to achieve BB and inform the source about it. Fi- nally, in full synchronization (FS) all nodes must simultaneously enter the state terminated after receiving the source message. The algorithms should be eficient both in terms of the time required and the communi- cation overhead they put on the network. We limit the latter by allowing every node to send a message to at most one neighbor in each round. We show that BB is achieved in time at most 2n in any n-node network and show networks in which time 2n−o(n) is needed. For ABB we show algorithms working in time (2+fi)n, for any fixed positive constant fi and suficiently large n. Thus for both BB and ABB our algorithms are close to optimal. Finally, we show a simple algorithm for FS working in time 3n.The optimal time of full synchronization remains an open problem.