<p><em> IEEE Transactions on Information Systems</em></p>

<article class="align-center media media--type-link media--view-mode-default"><div class="field field--name-field-media-entity-link field--type-link field--label-hidden field__item"><a href="https://doi.org/10.1109/TIT.2021.3123929" target="_blank">68(2),pp. 1119-1132</a></div>
      
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Group testing by nested pools

Group testing by nested pools - https://doi.org/10.1109/TIT.2021.3123929

Abstract<br />
In order to identify the infected individuals of a population, their samples are divided in equally sized groups called pools and a single laboratory test is applied to each pool. Individuals whose samples belong to pools that test negative are declared healthy, while each pool that tests positive is divided into smaller, equally sized pools which are tested in the next stage. In the (k+1) -th stage all remaining samples are tested. If p&lt;1−3−1/3 , we minimize the expected number of tests per individual as a function of the number k+1 of stages, and of the pool sizes in the first k stages. We show that for each p∈(0,1−3−1/3) the optimal choice is one of four possible schemes, which are explicitly described. We conjecture that for each p , the optimal choice is one of the two sequences of pool sizes (3kor 3k−14,3k−1,…,32,3) , with a precise description of the range of p ’s where each is optimal. The conjecture is supported by overwhelming numerical evidence for p&gt;2−51 . We also show that the cost of the best among the schemes (3k,…,3) is of order O(plog(1/p)) , comparable to the information theoretical lower bound plog2(1/p)+(1−p)log2(1/(1−p)) , the entropy of a Bernoulli (p) random variable.

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Group testing by nested pools

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