Group testing with prior statistics

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Abstract
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.

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