Randomized Communication Without Network Knowledge (1805.04842v1)

Abstract: Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is often best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. A large body of work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network $n$, and the diameter $D$), which may not always be realistic in systems with weak devices or gradual deployment. Very little is known about what can be done when this information is not available. This is the issue we address in this work, by presenting the first \emph{randomized} broadcasting algorithms for \emph{blind} networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in $O(D\log\frac nD\log^2\log\frac nD + \log^2 n)$ time, almost reaching the $\Omega(D\log\frac nD + \log^2 n)$ lower bound. We also give an algorithm for directed networks with collision detection, which requires only $O(D\log\frac nD\log\log\log\frac nD + \log^2 n)$ time.