  Mobile devices apply neighbor discovery (ND) protocols to wirelessly initiate
a first contact within the shortest possible amount of time and with minimal
energy consumption. For this purpose, over the last decade, a vast number of ND
protocols have been proposed, which have progressively reduced the relation
between the time within which discovery is guaranteed and the energy
consumption. In spite of the simplicity of the problem statement, even after
more than 10 years of research on this specific topic, new solutions are still
proposed even today. Despite the large number of known ND protocols, given an
energy budget, what is the best achievable latency still remains unclear. This
paper addresses this question and for the first time presents safe and tight,
duty-cycle-dependent bounds on the worst-case discovery latency that no ND
protocol can beat. Surprisingly, several existing protocols are indeed optimal,
which has not been known until now. We conclude that there is no further
potential to improve the relation between latency and duty-cycle, but future ND
protocols can improve their robustness against beacon collisions.
