Communication Problems in Random Line-of-Sight Ad-Hoc Radio Networks

The line-of-sight networks is a network model introduced recently by Frieze et al. (SODA’07). It considers scenarios of wireless networks in which the underlying environment has a large number of obstacles and the communication can only take place between objects that are close in space and are in the line of sight (are visible) to one another. To capture the main properties of this model, Frieze et al. proposed a new random networks model in which nodes are randomly placed (with probability p) on an n× n grid and a node can see (can communicate with) all the nodes that are in at most a certain fixed distance r and which are in the same row or column. Frieze et al. concentrated their study on basic structural properties of the random lineof-sight networks, like the connectivity, k-connectivity, etc., and in this paper we focus on the communication aspects of the random line-of-sight networks in the scenario of ad-hoc radio communication networks. We consider the classical ad-hoc radio communication model adjusted to the scenario of the line-of-sight networks and we study two fundamental communication problems: broadcasting and gossiping. We present three algorithms for these two basic communication problems in the random line-of-sight networks. The first algorithm solves the gossiping problem assuming that each node knows its location in the grid; it performs O(r4 p2 log n log r/ log(rp) + n/r) steps. Our two other algorithms work even in the model of unknown networks (a node does not know its location nor knows its neighbors and the topology of the neighborhood is unknown in advance). The first one is a distributed deterministic algorithm for broadcasting that runs in O(r4 p2 log n log r/ log(rp) + n/r) steps, and the second is a distributed randomized algorithm for gossiping that runs in O(r4 p2 log n log r/ log(rp) + n/r) steps. Our algorithms ∗Research supported in part by the Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, EPSRC grant EP/D063191/1.