  We consider the problem of quickly detecting a signal in a sensor network
when the subset of sensors in which signal may be present is completely
unknown. We formulate this problem as a sequential hypothesis testing problem
with a simple null (signal is absent everywhere) and a composite alternative
(signal is present somewhere). We introduce a novel class of scalable
sequential tests which, for any subset of affected sensors, minimize the
expected sample size for a decision asymptotically, that is as the error
probabilities go to 0. Moreover, we propose sequential tests that require
minimal transmission activity from the sensors to the fusion center, while
preserving this asymptotic optimality property.
