  We consider the problem of constructing a communication infrastructure from
scratch, for a collection of identical wireless nodes. Combinatorially, this
means a) finding a set of links that form a strongly connected spanning graph
on a set of $n$ points in the plane, and b) scheduling it efficiently in the
SINR model of interference. The nodes must converge on a solution in a
distributed manner, having no means of communication beyond the sole wireless
channel.
  We give distributed connectivity algorithms that run in time $O(poly(\log
\Delta, \log n))$, where $\Delta$ is the ratio between the longest and shortest
distances among nodes. Given that algorithm without prior knowledge of the
instance are essentially limited to using uniform power, this is close to best
possible. Our primary aim, however, is to find efficient structures, measured
in the number of slots used in the final schedule of the links. Our main result
is algorithms that match the efficiency of centralized solutions. Specifically,
the networks can be scheduled in $O(\log n)$ slots using (arbitrary) power
control, and in $O(\log n (\log\log \Delta + \log n))$ slots using a simple
oblivious power scheme. Additionally, the networks have the desirable
properties that the latency of a converge-cast and of any node-to-node
communication is optimal $O(\log n)$ time.
