Broadcasting in unreliable radio networks

Abstract

Practitioners agree that unreliable links, which sometimes deliver messages and sometime do not, are an important characteristic of wireless networks. In contrast, most theoretical models of radio networks fix a static set of links and assume that these links work reliably throughout an execution. This gap between theory and practice motivates us to investigate how unreliable links affect theoretical bounds on broadcast in radio networks.To that end we consider a model that includes two types of links: reliable links, which always deliver messages, and unreliable links, which sometimes fail to deliver messages. We assume that the reliable links induce a connected graph, and that unreliable links are controlled by a worst-case adversary. In the new model we show an Ω( log ) lower bound on deterministic broadcast in undirected graphs, even when all processes are initially awake and have collision detection, and an Ω( ) lower bound on randomized broadcast in undirected networks of constant diameter. This separates the new model from the classical, reliable model. On the positive side, we give two algorithms that tolerate unreliability: an ( 3/2 √ log )-time deterministic algorithm and a randomized algorithm which terminates in ( log 2 ) rounds with high probability.

The cost of radio network broadcast for different models of unreliable links

“…In this model combined with an offline adaptive adversary, global and local broadcast now require Ω(n) rounds, even in constant diameter graphs [11]. The closest matching upper bounds require O(n log 2 n) rounds for global broadcast [12], O(n) rounds for local broadcast. 4 See Figure 1 for a summary of these results and how they compare to the new results in this paper.…”

“…It is motivated by the ubiquity of unreliable links in real wireless networks. Existing results in this model [11,12,3,8] assume an offline adaptive adversary-the strongest type of adversary considered in standard randomized analysis. In this paper, we study the two other standard types of adversaries: online adaptive and oblivious.…”

“…A recent series of papers takes up this challenge by studying global broadcast [11,12], local broadcast [8], and graph algorithms [3] in the context of the dual graph model-a generalization of the graph-based protocol model that includes both static and dynamic links.…”

“…A defining feature of the dual graph model is that an adversary controls the behavior of the dynamic links (as previously argued [11,12,3,8], simpler assumptions, such as independent loss probabilities, do a poor job of capturing the unpredictable and sometimes highly-correlated nature of dynamic behavior in real networks). Applying the standard terminology from randomized analysis, this existing work on the dual graph model assumes an offline adaptive adversary.…”

“…This definition is strong and therefore, perhaps not surprisingly, most existing radio network results proved with re-spect to this adversary type are negative. They show, for example, that both global and local broadcast (defined below) require Ω(n) rounds [11,12] in constant-diameter graphs of size n. This is exponentially worse than the Θ(log 2 n) round solution of the static protocol model [2,8]. These lower bounds are not entirely satisfying as they leverage adversary behavior-such as basing link behavior on the outcome of private random choices-that is unrealistically pessimistic.…”