  We consider the problem of sensor selection for time-optimal detection of a
hypothesis. We consider a group of sensors transmitting their observations to a
fusion center. The fusion center considers the output of only one randomly
chosen sensor at the time, and performs a sequential hypothesis test. We
consider the class of sequential tests which are easy to implement,
asymptotically optimal, and computationally amenable. For three distinct
performance metrics, we show that, for a generic set of sensors and binary
hypothesis, the fusion center needs to consider at most two sensors. We also
show that for the case of multiple hypothesis, the optimal policy needs at most
as many sensors to be observed as the number of underlying hypotheses.
