  In this work we address the question how important is the knowledge of
geometric location and network density to the efficiency of (distributed)
wireless communication in ad hoc networks. We study fundamental communication
task of broadcast and develop well-scalable, randomized algorithms that do not
rely on GPS information, and which efficiency formulas do not depend on how
dense the geometric network is. We consider two settings: with and without
spontaneous wake-up of nodes. In the former setting, in which all nodes start
the protocol at the same time, our algorithm accomplishes broadcast in $O(D\log
n + \log^2 n)$ rounds under the SINR model, with high probability (whp), where
$D$ is the diameter of the communication graph and $n$ is the number of
stations. In the latter setting, in which only the source node containing the
original message is active in the beginning, we develop a slightly slower
algorithm working in $O(D\log^2 n)$ rounds whp. Both algorithms are based on a
novel distributed coloring method, which is of independent interest and
potential applicability to other communication tasks under the SINR wireless
model.
