  We consider a new group testing model wherein each item is a binary random
variable defined by an a priori probability of being defective. We assume that
each probability is small and that items are independent, but not necessarily
identically distributed. The goal of group testing algorithms is to identify
with high probability the subset of defectives via non-linear (disjunctive)
binary measurements. Our main contributions are two classes of algorithms: (1)
adaptive algorithms with tests based either on a maximum entropy principle, or
on a Shannon-Fano/Huffman code; (2) non-adaptive algorithms. Under loose
assumptions and with high probability, our algorithms only need a number of
measurements that is close to the information-theoretic lower bound, up to an
explicitly-calculated universal constant factor. We provide simulations to
support our results.
