Deterministic Broadcasting and Gossiping with Beeps

Broadcasting and gossiping are fundamental communication tasks in networks. In broadcasting, one node of a network has a message that must be learned by all other nodes. In gossiping, every node has a (possibly different) message, and all messages must be learned by all nodes. We study these well-researched tasks in a very weak communication model, called the beeping model. Communication proceeds in synchronous rounds. In each round, a node can either listen, i.e., stay silent, or beep, i.e., emit a signal. A node hears a beep in a round, if it listens in this round and if one or more adjacent nodes beep in this round. All nodes have different labels from the set {0, . . . , L− 1}. Our aim is to provide fast deterministic algorithms for broadcasting and gossiping in the beeping model. Let N be an upper bound on the size of the network and D its diameter. Let m be the size of the message in broadcasting, and M an upper bound on the size of all input messages in gossiping. For the task of broadcasting we give an algorithm working in time O(D+m) for arbitrary networks, which is optimal. For the task of gossiping we give an algorithm working in time O(N(M + D logL)) for arbitrary networks.