Broadcasting in udg radio networks with unknown topology

Abstract

We consider broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connected to all stations at distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message correctly) only if exactly one of its neighbors transmits at a given time step. One station of the network, called the source, has a message which has to be disseminated to all other stations. Stations are unaware of the network topology. Two broadcasting models are considered. In the conditional wake up model, the stations other than the source are initially idle and cannot transmit until they hear a message for the first time. In the spontaneous wake up model, all stations are awake (and may transmit messages) from the beginning.It turns out that broadcasting time depends on two parameters of the UDG network, namely, its diameter D and its granularity g, which is the inverse of the minimum dis- * tance between any two stations. We present a deterministic broadcasting algorithm which works in time O(Dg) under the conditional wake up model and prove that broadcasting in this model cannot be accomplished by any deterministic algorithm in time better than Ω(D √ g). For the spontaneous wake up model, we design two deterministic broadcasting algorithms: the first works in time O(D + g 2 ) and the second in time O(D log g). While none of these algorithms alone is optimal for all parameter values, we prove that the algorithm obtained by interleaving their steps, and thus working in time O`min˘D + g 2 , D log g¯´, turns out to be optimal by establishing a matching lower bound.

Broadcasting in UDG radio networks with missing and inaccurate information

“…The above described scenario was adopted in [15] (under the name of the spontaneous wake up model) with two additional assumptions. It was assumed that the nodes are aware of (a linear lower bound on) the density d of the network, which is the minimum Euclidean distance between any two nodes, and that each node knows its exact position in the plane, i.e., is aware of the exact values of its Euclidean coordinates in a global coordinate system.…”

“…Nevertheless, it is an important theoretical challenge to show that the above mentioned assumptions made in [15] can be removed without changing the optimal complexity of a deterministic broadcast.…”

“…We work in the above described model from [15] modified by removing the assumptions of density knowledge and of availability of exact positions of nodes. Instead, if the real position of the node is (x, y), we assume that the node perceives its position as being (x , y ), where (x , y ) is chosen by an adversary.…”

“…It should be stressed that we do not assume the knowledge of ε either. All other characteristics of the model are as mentioned before, and as adopted in [15]. In particular, the topology, size and diameter of the network are unknown to nodes.…”

“…It should be noted that our definition of time of a broadcasting algorithm is slightly different from that in [15] and the same as, e.g., in [6]. In [15] time was defined simply as the smallest round number t after which all nodes of the network have heard the source message.…”