Quantitative Group Testing in the Sublinear Regime
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The quantitative group testing (QGT) problem deals with efficiently identifying a small number of infected individuals among a large population. To this end, we can test groups of individuals where each test returns the total number of infected individuals in the tested pool. In line with literature on related inference problems, we consider the regime where the number of infected individuals is sublinear in the total population size. We derive a sharp information-theoretic threshold for the minimum number of tests required to identify the infected individuals with high probability. Such a threshold was so far only known for the case where the infected individuals are a constant fraction of the population (Alaoui et al. 2014, Scarlett & Cevher 2017). Moreover, we propose and analyze an efficient greedy reconstruction algorithm that outperforms the best known sublinear algorithm (Karimi et al. 2019) for certain sparsity regimes.
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