  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 {\em 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 $\{0,\dots , L-1\}$.
  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 $O(N(M+D\log L))$ for arbitrary networks.
  At the time of writing this paper we were unaware of the paper: A. Czumaj, P.
Davis, Communicating with Beeps, arxiv:1505.06107 [cs.DC] which contains the
same results for broadcasting and a stronger upper bound for gossiping in a
slightly different model.
