  The whitespace-discovery problem describes two parties, Alice and Bob, trying
to establish a communication channel over one of a given large segment of
whitespace channels. Subsets of the channels are occupied in each of the local
environments surrounding Alice and Bob, as well as in the global environment
between them (Eve). In the absence of a common clock for the two parties, the
goal is to devise time-invariant (stationary) strategies minimizing the
synchronization time. This emerged from recent applications in discovery of
wireless devices.
  We model the problem as follows. There are $N$ channels, each of which is
open (unoccupied) with probability $p_1,p_2,q$ independently for Alice, Bob and
Eve respectively. Further assume that $N \gg 1/(p_1 p_2 q)$ to allow for
sufficiently many open channels. Both Alice and Bob can detect which channels
are locally open and every time-slot each of them chooses one such channel for
an attempted sync. One aims for strategies that, with high probability over the
environments, guarantee a shortest possible expected sync time depending only
on the $p_i$'s and $q$.
  Here we provide a stationary strategy for Alice and Bob with a guaranteed
expected sync time of $O(1 / (p_1 p_2 q^2))$ given that each party also has
knowledge of $p_1,p_2,q$. When the parties are oblivious of these
probabilities, analogous strategies incur a cost of a poly-log factor, i.e.\
$\tilde{O}(1 / (p_1 p_2 q^2))$. Furthermore, this performance guarantee is
essentially optimal as we show that any stationary strategies of Alice and Bob
have an expected sync time of at least $\Omega(1/(p_1 p_2 q^2))$.
