Consensus and Collision Detectors in Radio Networks

Abstract

We consider the fault-tolerant consensus problem in radio networks with crash-prone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in single-hop radios networks, where all nodes are located within broadcast range of each other. In a novel break from existing work, we introduce a collision-prone communication model in which each node may lose an arbitrary sub-set of the messages sent by its neighbors during each round. This model is motivated by behavior observed in empirical studies of these networks. To cope with this communication unreliability we augment nodes with receiver-side collision detectors and present a new classification of these detectors in terms of accuracy and completeness. This classification is motivated by practical realities and allows us to determine, roughly speaking, how much collision detection capability is enough to solve the consensus problem efficiently in this setting. We consider nine different combinations of completeness and accuracy properties in total, determining for each whether consensus is solvable, and, if it is, a lower bound on the number of rounds required. Furthermore, we distinguish anonymous and non-anonymous protocols—where “anonymous” implies that devices do not have unique identifiers— determining what effect (if any) this extra information has on the complexity of the problem. In all relevant cases, we provide matching upper bounds.