  Development of many futuristic technologies, such as MANET, VANET, iThings,
nano-devices, depend on efficient distributed communication protocols in
multi-hop ad hoc networks. A vast majority of research in this area focus on
design heuristic protocols, and analyze their performance by simulations on
networks generated randomly or obtained in practical measurements of some
(usually small-size) wireless networks. %some library. Moreover, they often
assume access to truly random sources, which is often not reasonable in case of
wireless devices. In this work we use a formal framework to study the problem
of broadcasting and its time complexity in any two dimensional Euclidean
wireless network with uniform transmission powers. For the analysis, we
consider two popular models of ad hoc networks based on the
Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links,
and the other with randomly disturbed SINR. In the former model, we show that
one of our algorithms accomplishes broadcasting in $O(D\log^2 n)$ rounds, where
$n$ is the number of nodes and $D$ is the diameter of the network. If nodes
know a priori the granularity $g$ of the network, i.e., the inverse of the
maximum transmission range over the minimum distance between any two stations,
a modification of this algorithm accomplishes broadcasting in $O(D\log g)$
rounds.
  Finally, we modify both algorithms to make them efficient in the latter model
with randomly disturbed SINR, with only logarithmic growth of performance.
  Ours are the first provably efficient and well-scalable, under the two
models, distributed deterministic solutions for the broadcast task.
