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# Note on generalized group testing

Ilya Vorobyev

Submitted on 8 November 2022

## Abstract

In this note, we present a new adaptive algorithm for generalized group testing, which is asymptotically optimal if $d=o\left({\mathrm{log}}_{2}|E|\right)$, $E$ is a set of potentially contaminated sets, $d$ is a maximal size of elements of $E$. Also, we design a 3-stage algorithm, which is asymptotically optimal for $d=2$.

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Subjects: Computer Science - Information Theory; Mathematics - Combinatorics